Types of Errors (for the Post Mortem)
A real error occurs when you do not make the optimal play or bid, given the information available to you. The goal in bridge, aside from having fun, is to optimize your expected number of points. Or, put negatively, the goal is to avoid real errors. For example, if there is a 70% chance for your contract but you take a line of play that gives you only a 50% chance, you have made a real error. If a slam is very likely, given your cards and your partner's bidding, not bidding the slam is a real error.
Of course, you might bid a good slam and it goes down, or you might take the superior play and go down when everyone taking the inferior play is making the hand. That's just the way it goes; these are not real errors. To the contrary, the people who are taking the inferior play and making the hand are making the real error.
Unless one player is much better than another, it is not easy to diagnose real errors at the bridge table. Suppose your partner needed to lead hearts to set a contract and you know it. If he/she doesn't lead hearts, it is frustrating. But to claim your partner made a real error, you would need to know that the heart lead was best given what your partner knew. You can't put yourself in partner's shoes, because you know something different. Or, put another way, you need to know that the heart lead is the best, not just for the hand you just played, but for all the hands consistent with what your partner knew.
Double Dummy Errors
The second type of error I will call a double dummy error. Suppose you and your partner are defending a hand but do not set the contract. Afterwards, the declarer mentions that if you had defended differently, you could have set the contract. The declarer is not saying that you should have defended that way, so the declarer is not accusing you of a real error. The declarer is merely pointing out a double dummy error. Once, the only way I could have defeated a 3NT contract was to lead diamonds on the opening lead. Declarer and bid and rebid diamonds, and the dummy had supported them, and I had the king of diamonds, so there was no way I could know that diamonds was the killing lead and I did not make a real error, I made just a double dummy error.
Double dummy errors are potentially useful to learn about when they involve a play you didn't even think about. For example, once I defended a hand and realized afterwards I could have saved an overtrick if I held up with my ace. I still am not sure that I should have held up with my ace, given what I knew. But it was very interesting to think about, and subsequently I have been more aggressive about holding up my ace.
So there is a difference between the two types of errors in the post mortem. It is difficult to diagnose a real error, and not especially kind to point one out. A double dummy error is still sensitive, because it can imply a real error, but in theory by itself a double dummy error is not something to be sensitive about. On the hand I mentioned above, I almost didn't realize that the opportunity was there. So declarer would have been doing me a favor to point out that there was a way to save a trick.
In the bidding, a double dummy error is this. If you and your partner could have looked at both hands, and also known the opponent's bidding but not the opening lead, what contract would you want to be in? The contract you want to be in is the optimal contract, and if you aren't in it, you made a double dummy error. (Here, double dummy refers to knowledge of your hand and your partner's, not the opponent's.)
For example, if there are 13 tricks off the top in no trump, the optimal contract is 7NT. (The only other possibility is that the opponents bid, and then the optimal contract might have been to double them.) Again, just because you did not arrive in the best contract does not mean that you made a real error. Perhaps, given what you and your partner knew, you both quite accurately assessed that 7NT probably was not a good contract.
Still, it is useful to know what the optimal contract was. For example, if you are dummy and not paying attention, it is useful to know that you and your partner should have been in 4 hearts, even if it doesn't make.
The third type of error is a thinking error. Suppose you are defending and you do not count out declarer's hand. This is an error in thinking. If might lead to a real error. But even if you make the very same play that you would have made if you counted out the hand, and there was no real error, you still made a thinking error. Or, once I gave partner a suit preference signal, and he did not lead back the suit. I became a little angry with him. Now, as I gave my suit preference, I realized that it wasn't very obvious whether it was a small card or a big card unless he was paying very close attention to which spots had been played, and that I probably wouldn't know if I was in his shoes. Then I forgot that when he didn't lead my suit. That's a thinking error. Getting angry with partner is also a thinking error, and not thinking about why partner lead a different suit rather than the one I wanted was also a thinking error. When I later thought about the hand, I did not see how I could know to do anything differently than what I actually did. But I found my thinking errors and learned how to improve my future bridge playing.
Embarassing Vs. Ignorable Errors
Let me also discuss errors that are embarassing versus those that are ignorable. Suppose you have a 5-3 spade fit and you are deciding whether to play 3NT or 4 Spades. The norm is to play the 5-3 spade fit, so your partner will probably be upset if you bid 3NT and that doesn't work. If you bid 4 Spades and 3NT was better, your partner probably will not be upset. So if you bid 3NT, you had better be right; bidding 4 spades is safe. Similarly, if you are deciding between 3NT and your 4-3 spade fit, then you better be right if you bid spades. Your partner will not be upset if you bid 3NT and 4 Spades was the better contract. In fact, your partner probably won't even notice.
Similarly, in the bidding, doubling a contract that makes is an embarassing error. Not doubling a contract that goes set is an ignorable error.
In the play, it is often an error to play the ace when declarer leads to the KQ and plays the K. But it is an ignorable error. If declarer is leading to Kx, holding up the ace is an embarassing error.
If you are a normal human being, you try to avoid embarassing errors. So, you need to be very sure you are not going to make an embarrassing error, and you don't need to worry so much about ignorable errors.
But the score sheet doesn't care. An error is an error. A missed opportunity is a missed opportunity. A wrong judgment is a wrong judgment. So, it is a thinking error to be influenced by whether or not an outcome is embarassing or ignorable.
Actually, even at match points you usually lose more points for doubling a contract that makes than you gain for doubling a contract that goes set one trick. So you do need good odds in your favor before doubling. I don't know what they are. Maybe between 70-80%. But that still means you will be doubling contracts that sometimes make. If your opponents never make a doubled contract, you are not doubling enough.
So, do what you think is right. Do not be extra afraid of making embarassing errors, and do not be content with making ignorable errors. In the post mortem, don't beat yourself up for making an embarassing error. Your partner also must be sympathetic to embarassing errors, assuming your were just trying to make the best judgment.