After Adam's beating, the bruise/blood on the left side of his face disappears.
The bruise on Adam's back changes color from red to black and back to red between shots.
Adam has his blood tested every Friday, yet he has one on the morning of Lily's birthday, which is emphasized several times as being on Thursday.
When Michel and Adam are fighting in the alley, they start talking and Michel suddenly puffs on a cigarette that appeared out of nowhere, he didn't light it at any moment and then it disappears.
In the final cooking scene, Max's bandanna color changes from burgundy to blue to Frey and back, with him standing on different stations on the line all at the same time.
As famed chef Marco Pierre White has explained, a third Michelin star is a restaurateur's award. It is not given to chefs who don't own their own restaurant, so Adam could not achieve more than two stars working in someone else's restaurant.
The same shot is used at ~54:40 and then again at ~1:35:10 where the line cooks sit down for the "family dinner". The latter shot has Michel wearing the same outfit even though there are several actor passing in the foreground. Michel is no longer working in the kitchen at this point in the film.
When Anne-Marie gives Adam his mentor, Jean-Luc's knife roll, she says that her father had sharpened them just before he died. Later Adam when looking at the knives in his room, he tests the edge by running his thumb longways down the blade. An experienced chef would never run their finger along a real blade in that direction because it would have sliced his thumb open immediately.
Whenever Adam talks to Michel, he switches to French; it's barely understandable, but at least it's credible, given that Adam's not a native speaker. However, when Adam talks to Jean-Luc's daughter, Anne-Marie, they speak in English, even though she's supposed to be French. When she finally does say a line in French, it's gibberish for French audiences.
When Adam is screaming at his staff after opening night, he goes on for several minutes, but the clock in the wall reads the exact same time throughout.
When Adam is making the chocolate cake, he blows yellow powder onto the cake. A professional chef would never blow on food.
Adam is seen riding a motorcycle through London without wearing a helmet. This is against the law in the United Kingdom unless you are a Sikh.
Helene's tattoo (Sienna Miller's real arm tattoo) is missing in one scene but all the others are still there.
When Adam and Helene are standing next to each other at the service table, preparing the dishes for the Michelin Men in one of the final scenes, Helene is wearing a red headband. In several shots during the scene, Helene is also cooking on one of the stoves in the kitchen, not wearing the red headband.