Does the possibility of claiming tricks prevent the defense from profitting from declarer's errors?
Your question displays a gross misunderstanding of the capabilities of good players, even those merely the best in their club. At the club in Kingston where I mastered the game, the top 10 or 12 players could all remember the location of every significant card, for all 26 hands of a session, even several hours after a game. Once or twice a year the Director would be called in the auction of the first or second round with "This hand hasn't been shuffled since last week.", followed by an outline of where all the cards were in all four hands, and what contracts could and couldn't be made by both sides. 

Also, a sound claim must cover all possible lies of the cards that remain possible given the knowledge available when the claim is made. It is for this reason that claims are only rarely made when trumps are outstanding. However it is not at all unusual for expert players to claim and concede even endplays such as Throw-ins and Simple and Double Squeezes. At this caliber of play, those techniques are common place, and thoroughly understood by all parties. By the time the hands are well enough known for a sound claim to be made, there are no mistakes left to be made in the hand by any competent, never mind expert, player; any to be made are already history.