In my time in 5-star (or 4-star, or 3-star, depending on what city and whose stars) kitchens I have worked in, I have seen some doozies. The winner for me, I think, was a steamed sea-urchin custard that was steamed to order, as an appetizer (!!), in the sea urchin shell. It was insanely difficult to get the timing right. To be honest, I think the chef made a design mistake. No dish should be next to impossible to get right, in the moment. But I think the spirit of the question is more about which standard dishes are difficult. So here are some ones that I fear:
2) Paella: Rice, Chicken, Clams, Shrimp, Vegetables, Mussels… No two of those take the same amount of time to cook. And yet, all must be done at the same time, with just the right amount of brown crust on the bottom (no crust: not acceptable…. Black crust: worse). Bonus points if you are doing this the traditional way, on a wood fire.
3) Pâté en Croûte, with Inlay: The bread needs to be brown and crisp, and the forcemeat needs to be fully cooked, and the inlay of meat down the middle needs to not be overcooked. Especially, maddeningly difficult if the inlay is a piece of venison. It*s like juggling chainsaws, and the worst part is that you don’t know if you stuck it until a day after it’s cooked.