I am an Assistant Professor and I often see here many professor position opportunities. Besides publications, what usually Institutions look for when hiring an international candidate?
As being an international student in different countries, my understanding that - if your profile (Publications, Research collaboration) is really ground breaking (!!) - you don't need anything more. International Research Institutes and Universities will hire you straightaway if they have vacancies.
But if your publication and degrees are good and fair (which is true for 98% of the researchers), 'INTERNATIONAL NETWORK' is really really necessary.
People need to know you, international researchers/Professors should know who you are, what is your research field, etc. In a nutshell, besides publications and degrees from reputed universities, 'NETWORK' is the key. Attending good conferences could help you in this regard.
Along with the 'Networking', if you can demonstrate that you could possibly manage Grant in your new workplace for conducting research, is another crucial deciding factor. In this regard, having some previous big research grants is a PLUS.
It is difficult to answer this question since it depends a lot on the level of professor (assistant/associate/full professor, lecturer, reader etc.), the discipline concerned, and the country you are talking about.
In general, the following criteria tend to be relevant, but with varying relative importance:
publications, research experience
degree achieved: e.g. in Germany, you need a PhD or equivalent to become a professor. I some other countries, you may become a professor based on just a bachelor degree.
teaching experience
work experience: varies a lot with the type of institution etc. E.g. at a German University of Applied Sciences, you need 5 years of work experience, including 3 years outside university, to become a professor. At other universities, this is not formally required but in a discipline such as computer science, it would be very helpful to have relevant work experience
soft factors such as motivation, quality of your presentation and personal impression in discussion