After some thought, I was wondering if genetic mutations will be less frequent.
DNA is transcribed and transcripted via several enzymes (including DNA replicase, helicase etc), and this is when the mutations occur. Well what if there was a mutation in the DNA, and one or more of those enzymes were more accurate when copying or transcribing DNA - there would be less random mutations. This new DNA would be more favourable, as long as the environment was stable and devoid of major changes, as it would be copied more accurately compared to other DNA strands in other animals.
This would continue, and the enzymes becoming more accurate (other factors other than enzymes can be considered, e.g. the solution in the nuclear envelope, but I'll just stick to enzymes) until the probability of mutation is incredibly small.
This also offers a small explaination to the dinosaurs, because if they had less DNA mutations then they would be less likely to survive a major climate change.