I would have no problem insisting that any discrepancy in the wagered amount, be satisfied (within a percentage of the unmatched wagers e.g. 10%). As with any rule, each incident must be evaluated and governed by how the misunderstanding originated. For example; a player who insta-calls a wager will have no recourse if the wagered amount was misunderstood. Other situations, should offer some protection for a player that was misinformed, or in the case of a gross misunderstanding.
I do believe that a player going all-in that loses the pot, and is covered by the opponent, should never be allowed to play the next hand. The question then becomes; what happens to the extra chips? Small amount, within 10%...give to the winner. Larger amount, hmm...? I'm not quite sure, but I don't believe the loser (who's bet would have been covered by the opposing player) should be allowed to continue playing, unless there were a re-buy situation. The only remaining option would be to remove the chips from play.