Revealing mistake: When Lotte and Maxine are hugging by the side of the New Jersey Turnpike at the end, the camera pans around them and you can see shadows of the cover and poles holding it to protect them from the rain.Also at one point a large amount of water falls down which obviously pours off the cover.
Plot hole: The timing in the film is way off. Given the hours when JM Inc is open, most of the people there would only get to be Malkovich while he was asleep (yes, films have late-night shootings, but not every night); and Craig and Maxine stay up the whole time, then mess with Malkovich afterwards, then get in for work the following morning without showing any sign of fatigue even though there are less than 2 hours left for sleep.
Revealing mistake: When Craig (in John) is doing his dance of 'Despair and Disillusion' you can see the stunt double several times. The most blatant are when he jumps to the wall and lands in a press-up, when he does a forward roll, when he backflips and also when he slides against the wall at the end of the dance.