Recommendation letter has slightly wrong info – should I mention it in my cover letter? When I asked for the letter, last semester’s grades hadn’t been fully uploaded to the system so among the things my professor wrote, they said I was a top-5% student. This week, grades were updated and now I’m the top student in my cohort.

I don’t want to bother my professor again, and they might not respond in time for the deadline (Feb 1st). Would it be okay to add a small note at the end of my cover letter indicating my new standing?
If I was writing the letter, it wouldn't matter to me if you were the top student in your cohort; I still might list you as a Top 5% (or Top 10%) student. 

I've been asked to fill out similar references before, and I'm often asked if the person I'm evaluating would be considered Top 5%, Top 10%, Top 25%, etc. In my mind (unless stated otherwise), I am not being solicited for a precise numerical calculation based entirely on GPA or class performance; rather, I'm considering a myriad of other factors as well, such as reliability, attitude, professionalism, integrity, etc. 

You don't say what your letter is for (employment or graduate school), but, either way, the student who is top of my class academically (that is, the one with the highest average) isn't necessarily the first student I'd recommend for hiring – and I answer the "Top X%" questions accordingly. 

Moreover, your professor may not be evaluating you among the classmates in your cohort, but taking a more historical look at all the students he's ever had who have taken the class(es) you took. So, for example, if you took BWV 201 with me, and asked for a reference, I am going to evaluate you as compared to all the students I've ever had who ever took BWV 201 – not just the handful of students who happened to take that class with you last year, or the students you are graduating with on graduation day. 

Bottom line: I'd recommend that you be happy with the high rating you got, and stick with that.