--there is an infraction by an opponent that is minor and apparent to most even if uncorrected
--the aggrieved player claims to have fallen for the rather unlikely natural meaning indicated
--the Director is not called until well after the end of the deal
--there are blindingly obvious clues that things are not as the aggrieved player pictures them, or claims to have pictured them, but none of these causes a Director call
--in reporting the infraction, the aggrieved player will omit details that derail his case
--another reason for the bad score, unrelated to the infraction, often exists in the ensuing cardplay
--it soon becomes apparent that viewing the hand record is the catalyst, that the aggrieved player decides he was damaged, looks for the most advantageous bid not made, and convinces himself that with correct information that bid would have been made
I'm going to give you the latest example without all the pertinent details, as part of the exercise. (I tried to avoid pronouns until I got tired of writing 'the aggrieved player' and checking that my spelling of aggrieved agreed with the last time I typed it, so please accept he or his as being sexist but not necessarily indicative of the actual player....)

♠ 98
♥ T73
♦ AQT84
♣ Q64
Partner opens 1♠, RHO overcalls 1NT, and after you double, LHO bids 2♦ with no alert. Partner passes, RHO bids 2♥, and with LHO showing diamonds you decide not to compete further. 2♥ becomes the final contract and ten tricks are made, resulting in a very bad score. Our hero, as the auction in the next deal comes to a close, calls the Director with the helpful message "Unalerted transfer, I would have bid 2♠ with an alert."
It doesn't take long to find more holes in this argument than in a good piece of Swiss cheese:
--Partner had opened 1♠ in third seat, at favourable vulnerability. This pair's convention card showed that they played Reverse Drury and that in this position this could be a four-card spade suit. Coming in was potential suicide, especially after doubling the 1NT overcall with only eight points. Partner had a decent minimum opener that would be made in first seat and would probably raise, and certainly compete over a 3♥ call, after hearing this 2♠ call from a partner who had previously doubled the 1NT overcall.
--The 2♥ contract was defeatable after a spade to partner's ace, a spade back to the notrumper's king, a trump to dummy's queen and partner's ace (from ace-jack doubleton) and a spade ruffed by our hero. At this point a diamond lead would catch partner with Kx. A diamond ruff with the jack of trumps on the third round would be the sixth trick for the defense, and now a fourth round of spades would promote the ten of hearts to become the seventh trick for +200 and a near top. Even ace and a second small diamond to the king works, for a spade comes back for the same promotion; if declarer ruffs high with the declaring hand's final trump, you pitch your third club and declarer cannot get to dummy without allowing two more tricks to high ruffs. Unfortunately, partner, when in with the ace of trumps, lazily led a small spade for the trick four ruff when any spade would have had equal effect, and this indicated a disastrous club return, which led to two overtricks and a near bottom.
--The aggrieved player must have noticed after the opening lead that dummy, who had bid 2♦ apparently naturally, had six hearts and two diamonds. Table history shows that he did, comments were made. But if bidding 2♠ over a transfer completion was in the mind of our victim, it did not occur to the aggrieved player to call the Director until perusal of a deal record and some wishful thinking indicated that it would work.
Much of your skill as a Director is revealed in how you handle calls such as this. I learned what not to do from more than one club director who would loudly and conspicuously take the player's head and several other appendages and figuratively force the Swiss cheese upon them, advertising the details of the deal to the rest of the room. Entertaining perhaps, but not helpful. The much better way is to let the player know that you will have a good look and get them to continue play on the following deals, even if the whole thing screams of inanity. Very occasionally online you get a player who demands an immediate ruling and will not play until he gets one. That's easy. You simply tell him that you've always wanted to get the chance to play a few hands with his partner and that this is perilously close to happening.
The difficulty is in avoiding the temptation to clearly say what you know has happened: the player has gotten a bad result, looked at the hands and convinced himself that since 2♠ will make, he would have bid it with correct and timely information and everyone would have conveniently passed.
One way is to trot out that favorite of ACBL TDs, the 'experience or expertise' clause in the Alert procedure, 'Players who, by experience or expertise, recognize that their opponents have neglected to Alert a special agreement will be expected to protect themselves.' Another is the 'knows or suspects' clause, 'An opponent who actually knows or suspects what is happening, even though not properly informed, may not be entitled to redress if he or she chooses to proceed without clarifying the situation.' It's pretty clear from this that our hero should have called when dummy hit.
In this case, my choice was to simply point out to him that had he called when dummy appeared, I could have asked him at that point what he would have done, forcing him to answer before seeing the other 26 cards. This appeared to make the point quite nicely and no further argument came back. If it had, I would have told him that 2♠ would probably lead to more bidding, even quite possibly from partner, and Id have pointed out partner's elementary defensive lapse that led to the bad score.
So what shall we call this type of director call? The Cherry Pick? The Holey Moley? The Printout Problem? The Captain's Complaint (since the aggrieved party morphs from Captain Oblivious to Captain Obvious as the hand record makes it clear what he would have done)? Respond with a better name if you come up with one!
I think it is great that players see the deals after the play if they wish, I don't want that to change. I do hope that we TDs will watch for this particular ploy and make sure we don't fall for it.