These concerns were mentioned in the comments (now in the chat room linked from a comment):
This, unfortunately, looks like a "make a big list" question that likely too broad for effective answers.
In this community, the consensus is generally against big list questions
That is the reason your question was closed. Making the scope of the list narrower (by specifying the field, or specifying the part of the application you're asking about) doesn't help; the fundamental question is still asking us to compile a list. When a question is posed in such a way that it can't be answered well in one answer, but needs many separate answers to give a complete answer, it is "too broad", even if the situation referenced is very narrow. This community has decided that we don't want those kinds of "list" questions (with some exceptions, that are discussed on meta before the question is posed).
You also make the situation a bit worse by asking for people's opinions about which mistakes are most serious. (See the help center.)
Your question could be improved by framing it to be about your specific situation, instead of asking for a list of anecdotes from other people's situations, and by not soliciting opinions. Instead of
In your opinion, what are the most serious common mistakes that continental European candidates for tenure-track assistant-professor positions in Computer Science in the US commit in their cover letters?
You could ask,
I am a continental European candidate applying for tenure-track assistant-professor positions in Computer Science in the US. What common cover letter mistakes are made by people in this situation, that I need to watch out for?
This could potentially have a single "best" answer, and doesn't ask for subjective opinions on which mistakes bother people the most. The "best" answer would not just be a one line answer enumerating a mistake that has been judged "most serious" by the votes of other users; the "best" answer would be a comprehensive answer that describes the common problems and explains more about them.