The last mistake I want to highlight is drawing attention to your weaknesses.
In an interview, you want to be prepared to address your weaknesses if asked. But in a cover letter, you have the floor. This is your opportunity to sell yourself. So don't waste any ink on things that don't promote you as a candidate.
Most often, I see this mistake crop up with words like "although" and "despite," as in "Although I have just graduated…" or "Despite my lack of experience in this field…"
Resist the temptation to use these words and phrases and go straight to the good news. Even if you're concerned that you don't have the right degree for a position, there's clearly something that makes you think you'd succeed in the job, or you wouldn't be applying for it. Talk about that. Emphasize whatever it is that makes you a stellar candidate, so even if the hiring manager does have a concern about something on your resume, you will have already convinced them to give you a shot and bring you in for an interview.
You don't know whether the hiring manager will even consider something a weakness, but you want to avoid signaling that you consider it a weakness. (And a big enough one to mention on your cover letter!)
In the worst case scenario, the hiring manager will have completely missed whatever it is (your age, your lack of experience, your degree) or will not have considered it important, but will now reconsider whether to exclude you from the interview pool because of it.
So avoid drawing attention to anything that might be considered a weakness. And after writing a cover letter, go back through and look for those tricky words and phrases: although, despite, even though. Cut them out and leave only the good stuff.