I just finished an internship and my boss gave me a very nice reference letter. While I'm happy with the content, I found one spelling mistake and it is really bothering me. Should I tell him to re-write it or just live with it?
There should be no embarrassment about asking a colleague or even a boss to correct a spelling mistake. We are all human and we all make mistakes. Wrap it up with a note of thanks for producing a nice reference letter and it doesn't have to be a big deal.
Letting it slide however could be a problem. If it is likely that any reader of the letter would notice the spelling error then it could put the opinion of your boss in doubt. Similarly if the reader of the letter knows that you have read the letter (because you forwarded it to them) then it could reflect badly on you for not getting it corrected.
So, in summary, ask your old boss for the mistake to be corrected, but do it tactfully.
You might ask him to correct a typo or two. Given the number of errors, I think you should let it go. He has already done you a favor by writing it.
However, you shouldn't send the letter as part of your initial contact with a prospective employer. That might give the wrong impression that you see no faults in the letter. If someone asks for references, send it, but tactfully mention his lack of fluency:
Here is a letter from my former supervisor. We had a great relationship, but he is not fluent in English.
Not for a reference letter, but I've corrected typos in what my manager wrote for my appraisal. I've done this with three out of the four managers I have had. (The final one didn't have any typos.) Two of them were non English speakers so it was easier for me to notice than them. The other made a genuine typo. None of the three seemed to mind me pointing it out and two thanked me.
I don't think it is bad to ask for the correction; you said it is only one error so it isn't going to embarrassing. Remember that the letter reflects on your boss too. He would likely rather not have his typo/lack of English knowledge shared with whomever you show the reference letter to either!
I would pretty much live with it if it is minor. If it is the only problem with reference letter, it is even less of a reason to change it. Unless of course, the spelling mistake relates to some important information such as your details, or your job information. If you look close enough to any document, the chance of find an issue with it is usually quite high.
If you really want to get it change, read the rest of the reference letter to determine what else you want changed and submit those changes in one request. That way, your boss would be more likely to put some effort into making those changes in one hit.