As an occasional playing club director myself, I think I would encourage players to call, even if I am about to play the board -- instead of placing a question mark.
Even a playing director can usually tell it is a scoring error while approaching (because the North player is waving or looking puzzled at the traveler) and note that the board has yet to reach him -- now you can simply ask for the board number and line (or N-S pair) number, and check it when you play it. Or, as is usually the case, it is the most recent North that has made the dubious entry, so you get the player to make the enquiry when the round ends.
Even if it is a serious problem and the TD needs to do some immediate investigating, you can recruit a substitute or simply give A+ to the opponents when the board gets to you (and decide whether you want to fine the offending North player as compensation). Better this than trying to work out what a mysterious question mark may mean at the end of the game.
If "reasons for traveler question marks" were made into a question on Family Feud, the survey results would be something like:
22 - Wrong Vulnerability
18 - Score entered on Wrong Side
14 - Score Correct but Illegibly or Ambiguously Written
11 - Missing Asterisk(s) for (Re)Doubled Contracts
9 - Number in Wrong Column (between "Making" and "Down")
8 - No Discernible Problem but Every N-S After the Question Marker Blindly Assumes There Is One Somewhere
7 - Declarer Initial Letter Wrongly or (usually) Illegibly Entered
5 - Somebody Scored On My Line, so I'll Let You Figure Out Who and Score Way Down Here (Someone will follow along blindly compounding the problem)
4 - Wrong E-W Pair Number (most N-S players are trained to ignore this one)
2 - I Hate Travelers So I'm Going To Enter The Score But No Other Details At All
Yes, I have encountered the last type. They are astonished to discover that they have earned a N-S ban when they are assigned E-W for the next seventeen weeks and ask why.