Looking at the artwork of Vecna that came with the dossier, he appears to have both eyes and both hands, which I thought were supposed to be missing. Is this an oversight by the artist, or am I missing something?

It appears the hand in the art could be artificial, but the eyes look the same.

Probably because the artwork and statblock are to represent Vecna before Kas betrayed him (it was Kas who cut off his hand and cut out his eye). 

But if that doesn't suit you as a lich he is able to reform his body - hands and eyes included - when he dies and unlike other lichs doesn't even need a phylactery to do so. So you can always just say the artwork is post reform. 

There's also the Regenerate spell which he could easily gain access to given his vast network of cultists across the multiverse.