Plot hole: There is no logical reason to switch off the Bombe at midnight when the codes change. Firstly, Turing's proving the concept of automated code breaking, so even if it only finds the right settings days or weeks later, the experiment is worth doing, then you can work out how to speed it up to be operationally useful. Secondly, even in steady state operation, cracking "yesterday's" settings (and thus intercepted signals) is still going to be pretty useful in most cases. Threatening to smash the Bombe up at midnight is good stuff to add some movie tension but, in reality, it's nonsense.
Character mistake: In the movie it is stated that "There are 159 million, million, million possible Enigma settings. All we had to do was try each one. But if we had 10 men checking one setting a minute for 24 hours every day and seven days every week, how many days do you think it would take to check each of the settings? Well, it's not days; it's years. It's 20 million years." This is massively understating it - if it would take 10 men only 20 million years to check all the settings of Enigma they would have to each check 251,861 combinations per second. (00:15:04 - 00:16:46)
Factual error: At the one of the movie they say "Turing's machine" inspired generations of scientists. "Today we call them computers" suggesting he invented the computer, which is wrong. Despite there being different opinions. The first computer was built around the beginning of the 20th century. It's very far fetched to claim he inspired the modern computer, if not bogus. (01:50:10)