I think The main theoretical problem with most approval and range voting methods is that they fail the Condorcet and majority criteria. A candidate who is preferred over every other candidate by a majority of voters can lose, which sucks, but in practice it is debatable how common such an occurrence would be.
But it turns out that approval voting is itself considered a very good voting system (I remember reading an article about how a conference of experts voted on their favourite voting systems and approval voting won, but I can't find it because "voting system vote" isn't a very good Google search).