It’s not necessarily down to “mistakes”. There is a set of admissions criteria that you have to meet to stand a solid chance of actually getting an offer and this can vary by subject.
I’m a successful reapplicant (for Chemistry at Oxford) - there were definitely mistakes made on both occasions when I applied, but I feel that there were things I did before the second attempt which helped me get in. Since the mistakes were largely made during the interviews and there is a code of conduct that I don’t overly want to breach, I won’t share them.
After getting the rejection the first time, I immediately requested feedback and once I got it, I found that I had underperformed slightly in my interviews and was barely above the average offer holder in terms of the strength of the UCAS application.
I prioritised working on things that would help my problem-solving, critical thinking and capacity to articulate my thoughts clearly. This included getting mock interviews from some Oxbridge graduates, mentoring classmates and answering chemistry questions here on TSR. This definitely made my interview performance this time round more convincing, but it was still far from perfect.
To strengthen my UCAS application and personal statement, I also participated in the 2022 Chemistry Olympiad (even getting into round 2, which I reckon is largely what got me the offer this time round) and took the AEA in mathematics (which is because a strong aptitude for maths forms part of the admissions criteria for chemistry at Oxford).
So although this isn’t what you initially asked, focusing purely on the “don’t’s” when applying to Oxford/Cambridge will not help much when you haven’t necessarily established what you should be doing.