1. Finality of the Prophet of Islam is a position that infringes the domain of Allah, has Allah finished everything with humanity with the seal of the prophethood in the person of Muhammad. If this is the case then immensity of Allah himself is in question. The seal of the prophethood in Islam makes the activity of Allah limited to a particularity, the universality of Allah and his/her message cannot be particularised, even if such is made then it is historically cannot be final as Allah is infinite as per Islam and other monotheistic traditions.

2. The place of Qu'ran in the theological scheme of Islam. Al Qur'an is the word of Allah and not Allah himself. Any undue place to Qur'an violates the concept of Tawhid. How do Muslims wish to deal with these two areas of theological concerns.

3. The Worship ritual around Kaaba and the worship of One God with no other. If Allah is worship worthy then the Kaaba ritual seems a discrepancy in the world of theology and ritualism. 

The concept of Jihad in relation to terrorism. Theologically, not politically, is terrorism as used by Al Qaida and Boko Haram the right method for Jihad?

MR. Shanthikumar Hettiarachchi's answer doesn't answer about theological controversies within global Islam: Finality of the Prophet, and The Worship ritual aren't matter of real controversies within islam.

The concept oh Jihad not either. This concept is secondary and appears and occasionally appears in times of crisis  (this is now a great political problem, but for theology it is very clear : a Great Jihâd is a personal effort to better (The most excellent jihad is that of the soul) and  a secondary Jihâd refers to a defensive war( Fight in the cause of Allah those who fight you, but do not transgress limits))

Great controversies are:

                       Between SUNNI and IMAMI

                       Predestination (Qadar) and free will 

                       Createdness of the Qur'an ( Mu`tazila) or not  (Sunni)            

Ivan,  Between Sunni and Imami  or Twelver Shi'a Islam or Imamiyyah  is a problem of Tradition  (Fathima , Ali and other Imams) not primarily theological. It has been built in as a theological issue both for Sunni and Shia tradtion. At least Muslims refuse to accept that position which I can understand. The real theological issue  is the notion of Tawhid and the primacy of the Al Qur'an as I noted before which some Muslims cannot see, perhaps you do not see it as well. Also my other two points in the trail. They have become deeply theological.  Ritual is based on theology I am afraid. Theology gives meaning to ritual and the ritual affirms theology. They are bed fellows phenomenologically.

Dear Shanthikumar, we agreed for one important point. I agree that the real theological issue is the notion of Tawhid and the primacy of the Al Qur'an : that is the question of uncreated Qur'an , so i've said in my answer

For the fact that ritual is based on theology, I may agree, but not that it made a controversy within islam. Or, may you tell us we are talking about it ? I don't know them.

 About Sunni and Imami , it is more than a problem of tradition. It has evolved into a real theological controversy,  near what you meant by ""Finality of the Prophet" ." The "seal of the prophets" ( Khatam al -Anbiya') is challenged by the role of Ali (for Imami), the hidden Imams , the Batiniyya ( "secret meaning" of the Koran  for Imami ),  and the theological imami's concept of the Mahdi .

Moreover, if we consider that some Sunni (minority ) discuss on the meaning of this concept, we can actually put this theological problem among the three discussed . We would be on agreement for two points, finally

Current controversies: Shi`ah vs Sunni, rationalism/reformism/traditionalism, ijtihad vs taqlid

I think the answers provided indicate problematic situations within Islam.  AT this time, there is not a unified Islam, an "ummah" or community of believers who agree about much of anything.  If we include the Sunni/Shi'a schism as a major theological issue within Islam (and it surely is), then that is a problem that truly lies within the faith of Islam and its followers.  But perhaps it would be easier to respond if the questions were more narrow in respect to the focus you want.  For instance, I personally agree that jihad in relationship to terrorism is a theological, political, and every other kind of problem area within Islam and in relationship of Islam to the rest of the world. To some Islamists, jihad is a "sixth pillar" of Islam; that becomes a theological question that goes  to the Qur'an and the Hadith and the interpretations provided by the great theologians, schools of law, etc.  But if we include the theological questions within Islam, then we are going to be loaded with the controversies among the Shi'a with the hidden imam, the Mahdi  ( as Ivan points out), and the numerous minority sects of Islam.

I would like to see Jihad treated theologically by the present-day scholars of Islamic jurisprudence because it is such a huge issue. Presently, ISIS and its leader Al-Baghdadi are making theological claims to the Caliphate and to the religious obligation of Muslims to gather under his leadership.  That is a call that needs to be answered by those qualified to speak to the theology and tradition of t he Caliphate and to the teachings about the End Days.  This issue of global Islam is vital today and does need to have some priority over the internal questions.

Personally I agree most closely with Suleman especially on reform vs. revolution vs. tradition.  Perhaps Salafist vs. Islamist (how close are they theologically on issues of reform and revolution?). Ijtihad is a HUGE issue and completely denied by the present-day Islamists, who seem to forego 14 centuries of Islamic jurisprudence, rationalism, intellectual tradition, etc. in favor of a return to the 7th century world of Medina, interpreted only as they see fit.

A classic text written on these issues is The Great Theft: Wrestling Islam from the Extremists by Khaled Abou El Fadl.  Another to read is Enemy in the Mirror by Dr. Roxanne  Euben.  Her discussion of the approach developed by Hasan Al-Banna and Sayid Qutb can help to clarify the controversy of rationalism/reformism, etc. These political issues are theological to Muslims and since we lack an Islamic global leader who can speak from a legitimate position, we desperately need to hear from the moderate Muslim scholars who know and interpret the texts of Islam.  Right now Al-Baghdadi is claiming that legitimacy and establishing an alleged "Islamic state/nation" from which he claims he can speak with authority and issue fatawa that Muslims are obligated to follow.  That claim is both political and theological--but then Islam (as so many point out) is a lifestyle that combines religion, politics, theology, etc.  Politics is, then, a subject of theology.

Al- Baghdadi is a Muslim cleric, with a deviant view of Islam,  he does not represent Islam at all with his preaching embedded in violent discourse. So leave him to be isolated by his apocalyptic ISIS criminals. The are renegaded by other Muslims to be non Muslim, de facto they are Muslims which is what these other Muslims also fail to fathom.

We must understand that Muslims are going through an enormous difficulty socially and politically. The major problem within the Muslim world is that it has lost the intellectual capacity debate from a perspective that is admissible to right thinking counterparts of other perspectives. When one commences one's discussion that is the 'other' is wrong then such a discussion cannot go far. Islam is rich with an  Intellectual acumen but there is a dearth of erudition to deploy critical thinking within the discourse even though the Islamic narrative is 'peaceful' and has a message to the World. And it is being hijacked by groups of armed men who sometimes even cannot obey their own parents let alone Allah.  They bring shame to such a historical faith.

The compilation of the Holy Quran by mortals. Lets remember that the Prophet of Islam  did not compile the Quran and at the time of the revelation of the verse saying "This day, I have perfected your religion for you, completed My favor upon you, and have chosen for you Islam as your religion" (5:3)  the Quran compiled as it exist today, did not exist. Yet the religion was perfect.

While other copies of the revelation were destroyed, how would the "Ummah" react to findings of contemporary manuscripts having variances to the present text.

From time to time in history, such texts have appeared and have been dismissed with a variety of explanations, not always convincing. At a time when communication of any discovery takes only seconds to reach the other end of the planet, and the billion plus Muslims,  how will various Islamic communities react to such discovery.

I have no idea

Well, I am wondering where to recommence this discussion, as I was away from it for a while. I basically have said what I wanted to say about the theological issues. However, the real issue might be also the human incapacity to recognise DIFFERENCE that even Allah in the Qur'an has reiterated. The problem is that each Muslim group takes both Allah and the Al Qur'an on to their own lap of interpretation. What is strange is that the prophet is left alone  in the desert with ISIS prophets now preaching to the world of a new Islam with no regard at least to the Medina constitution which is part of the hadiths of the prophet of Islam. Actually ISIS and similar groups have destroyed the spirit of Islam. Nothing from outside can destroy Islam or for that matter any ideology, but from within. The classic example is what Al-Qaeda and ISIS have done to Islam. Today's crisis is not so much theological but stupidly political. 

there are several controversial rule in the Islamic theology, but before I mention 3 of them, let me clarify that those controversial rules have been produced by the reason of misconception regarding the taught Islamic rules including many people implement them in an abusive method then coming a several misconception about Islam.

three of several controversial rules in Islam (in the most of non-muslims point of view)

1. the Implementation of Jihaad

2. Islam has spreaded by sword

3. an order to kill each non-muslims every where

these are three of several misconception regarding Islamic theology. In order to find a more explanation about those three points above, allow me to provide you a reference in order to find a detail answer for those 3 points of misconceptions.

http://icems.event.uinjkt.ac.id/wp-content/uploads/2018/05/PROCEEDINGS-ICEMS2017-watermark-.pdf

open the file and find out my full name and read the article,

hope that answers your question

You are still on just one single concept (Jihad) which has several interpretations, understandings. Butt he real issue that I originally raised was different.

It relates to the fundamental theological position, Jihad is no fundamental of Islam if you read it carefully like Tawhid (natuer of Allah), finality of the Nabi, centrality of the Godhead and the almost giving primacy to Al Qu'ran and the Kaabah ritual. These are both theological and ontological to the concept Sacred and Profane ( Mary Douglas), hobnobbing the practical. Hence, my interest as a phenomenologist to query. I have no intention of focusing just on Islam, I would do the same with other tradition, In fact I have done so with other traditions ad experimentum which is what I am interested in.