Is either player at a disadvantage when cards "aren't' shuffled well enough"?
As long as neither player has information about the order of cards in a deck of cards, no player can gain an advantage from a "bad" shuffle.

A "bad" shuffle could be defined as a shuffle that does not, by a reasonable standard, erase all information remaining from the end of the previous game, most notably the order of cards. This does not mean that there is no recognizable order to the cards, only that neither player knows in what order the deck is, including after a player has seen a part of the deck. 

If a particular game produces long streaks of ordered cards on the table, and a subsequent shuffle before the next game does not break up that order, then there is the potential that information remains to be gained in the next game, and a possible advantage for one player. The amount of shuffling needed to prevent that depends on the technique used and the amount of order that is present (e.g. how large are the blocks of ordered cards the game typically produces).

As for your problem with the half-serious allegations of negligience or even cheating by your wife: That question is not likely to be resolved with better shuffling alone, it's about venting her frustration after losing - she is not going to complain about a bad shuffle if she wins. Simply offer to let her shuffle the deck whenever she wants, or at least let her cut the deck before the game starts. This involves her in the shuffling process and she has no more reason to take insufficient shuffling as an excuse.