Consider the following:
An Orc takes the attack action against a PC with an AC of 18. The DM rolls in front of the screen and gets a 14. He silently adds the +5 bonus from the Orc and announces that the attack hits.
Pretty basic. Now consider the same situation, but with a Lore Bard in the party:
An Orc takes the attack action against a PC with an AC of 18. The DM rolls in front of the screen and gets a 14. The Lore Bard sees the 14 and, while not sure of the exact attack bonus for the Orc, assumes that is should hit his companion. He therefore uses Cutting Words and in the end, the attack misses.
Okay, so here the DM had to wait for the bard to decide before announcing if the attack hit, because "you can choose to use this feature after the creature makes its roll, but before the GM determines whether the Attack roll or ability check succeeds or fails". Simply having a Lore Bard in the game changes how the DM does his rolls.
But what if the attacked PC has the Shield spell prepared? Shield takes "1 reaction, which you take when you are hit by an attack". Usually the DM will roll behind the screen and simply announce if the attack hits or not, letting the PC choose to Shield or not. Telling him the die roll would be meta information about whether or not the Shield will be wisely used or not.
So having a PC with Shield in the party forces the DM to roll behind the screen. But the Lore Bard needs to know the number on the die in order to decide on it's Cutting Words! And if the DM asks the PC if he wants to use Shield because the attack hits, then it's too late for the Lore Bard to use Cutting Words!
It seems to me that the DM must be aware at all time of the PC's reactions that must be done in a specific window, to ensure that he presents the information in the right order and that he allows enough time for the player to decide.
How can a DM deal with this?
Bonus points for giving particularly problematic abilities to watch for when resolving an attack roll.
I am not interested in a list of all features that grant advantage/disadvantage or a bonus to a roll since most of those are resolved prior to the attack and are not step sensitive. For example, if the DM forgets to remove a d4 from a 'Bane'd creature, the reduction can still be applied afterward.
Shield and Cutting Words are particular because they must be used between some steps and are affected by yet unknown information (actual die roll and attack bonus, respectively).
Often times it is pretty obvious when the player will use Cutting words or similar features. When my evil sorcerer is about to cast a powerful spell the PCs identified I ask if the Bard wants to cast cutting words.
Similarly, if a player is very low on HP, I ask. I usually wait a bit before declaring if the attack hits (I use the time where I'm explaining the action narratively to see if the party member wants to use their reaction) And yes, it is good to know what reactions are available for your party; however, you could also simply ask if anyone wants to do something after an attack roll.
Lastly, Don't be afraid to retcon the story as long as the player using their reaction made sense; you don't need to punish them unnecessarily.
Note: I removed the list of some relevant class features, since some might perceive it to be too selective and unhelpful; the edit log still carries the list if you are interested
I have a bard in my own party. I use a GM screen (most of the time). What we do is I announce the total number "(14+5) = 19!" Then he decides. I try not to be too much of a stickler if the PC wants to give a side-glance at his wincing buddy for whether or not he should use it.
What I don't do, is ask the player after every action whether he uses it or not. If there is a short delay, then I lean in their favor. Since I often use the average damage, they know how much they take and I can "roll back time" a few seconds.
I've always interpreted the writing of the cutting words feature to mean you make the decision after the creature decides who to attack but without seeing the roll.
The ordering then, for me, would be:
In my personal experience, it doesn't really break the game to take away the decision factor of whether or not cutting words or shield will be useful. A quicker version could then be:
Of course this gives more power than intended to the cutting words and shield features but I don't think it's too much in the long run.