www.movie-mistakes.com have a few scenes listed that were mistakes in "continuity" during the making of the film.

When they are driving back home from the holiday cottage you can clearly see an M25 sign in the background. The M25 didn’t exist in the 60s.

Withnail’s car is an ancient, battered, rusty Jaguar which looks about 20 years old. However it is H registration and so would have been brand new when the film is set.

In about the penultimate scene of the film, Paul McGann packs his suitcase ruefully, placing a copy of ‘The Adventures of Huckleberry Finn’ on top of his piled clothes. On the paperback’s cover, there is a sophisticated reproduction of a painting of a steamboat. Such printing techniques were far beyond the capabilities of Penguin Books at the time the film is actually set, when the standard cover would have comprised a series of white and green/orange bands.

In some scenes, bar-codes are visible on cola cans – bar-codes weren’t around in the 60’s.