Mew having the DNA of all the pokemon doesn't seem to affect the game... Mew has two great advantages:
1) His total stats are pretty high, plus all his stats are evenly distributed.
2)He can learn all the TM and HM moves.
That also means he can be trained in many types roles. Sometimes, he's strategy is near unpredictable or unexpected.
Something I noticed long ago that doesn't make me kinda happy... Most decent Ice Beamers (Dewgong, Articuno, Suicune, etc) have average to low speed, thus giving Dragons a one-turn advantage. In a one-on-one fight, it may not be much of a huge advantage, but it amplifies in team battles, where BPers are around. Then again, (if I'm not wrong) all ubers except Mew (GSC glitch) and Celebi can't learn BP.