unless you are extremely lucky a primer set will always anneal to the wrong place to a small extent. Sometimes even a single primer will anneal facing itself annealing randomly in the wrong position. Every 10 cycles of pcr generates 1000 times more product so 30 cycles may generate up to 10exp9 amplimers. Usually of the correct amplimer but often with a little of the wrong amplimer. If you now do another pcr with the same primers even the small amount of wrong amplimer will be amplified 1 million times if you run 20 more cycles. There is also a risk of there being so much amplification second time round that the product anneals to itself and extends in long concatomers because it is in excess compared to the amount of primer.

If you use nested or half nested primers for the second round pcr then the wrongly amplified material probably does not contain the sequence allowing the nested primers to anneal so that only the correctly amplified first round product can amplify so the nested product is usually very clean even though the nested primers may not be as well designed as the first set this is not important as the target genome is now only a thousand bases or less. Use nested primers where possible .They are very cheap and will produce cleaner results

unless you are extremely lucky a primer set will always anneal to the wrong place to a small extent. Sometimes even a single primer will anneal facing itself annealing randomly in the wrong position. Every 10 cycles of pcr generates 1000 times more product so 30 cycles may generate up to 10exp9 amplimers. Usually of the correct amplimer but often with a little of the wrong amplimer. If you now do another pcr with the same primers even the small amount of wrong amplimer will be amplified 1 million times if you run 20 more cycles. There is also a risk of there being so much amplification second time round that the product anneals to itself and extends in long concatomers because it is in excess compared to the amount of primer.

If you use nested or half nested primers for the second round pcr then the wrongly amplified material probably does not contain the sequence allowing the nested primers to anneal so that only the correctly amplified first round product can amplify so the nested product is usually very clean even though the nested primers may not be as well designed as the first set this is not important as the target genome is now only a thousand bases or less. Use nested primers where possible .They are very cheap and will produce cleaner results

This was nicely addressed by Paul Rutland.

I would just add that nested PCR has exquisite sensitivity, and the potential to produce very clean signals- especially with properly designed primers. Beginning in 1991, I used this technique successfully (and other techniques described in my published papers) to make Preimplantation Genetic Diagnosis-- based on biopsies of individual human embryonic cells-- a reliable technique. In our lab, we had zero misdiagnoses in the eight years that elapsed from the time that I first set up the lab to the end of my tenure as director.

As Paul and Gene explained, Using a nested primer you can selectively amplify your gene of interest from a pool of PCR products amplified in your primary PCR. As you mention, if you use the same set of primers used for your primary PCR for your secondary PCR, two possibilities exist.

1. The same set of primers may not anneal to the PCR products and will not result in any PCR amplification or can give a smear instead of clear bands (I faced this problem).

2. Since, all the PCR bands have the same sites, it will amplify the bands again without specificity and again result in smear.

So always try to amplify the secondary PCR with a nested primers (internal of primary expected product) or at least one primer (either forward or reverse) internal of your primary gene product that can give more specificity for the amplification.

Good Luck