Answer:
Well, a lot of it is in speculation right now, but one disadvantage has to do with telomeres.
At the ends of each of your chromosomes there are long 'buffer zones' where there are a lot of nucleotides, but no actual genes. These are called telomeres Everytime your DNA replicates during cell divison, bits of these buffer zones break off. This is okay, because again, it these 'buffers' don't carry any information. The problem is, eventually you DO start loosing information because the telomeres run out. This is linked to aging.
Dolly the sheep, for example, died at only age 6 (most sheep live to be about 2) and one of the things that they noticed was that she had shortened telomeres, because her chromosomes originally started from an adult sheep; they hadn't been brand new at her conception.
As it turned out, she had problems like arthritis and such that you would expect from a much older animal