How long will a 30 day late payment stay on my credit report?

Up to seven years if you do nothing about it. There is no minimum reporting period though, so even if it reported accurately (ie. not a mistake), there is still a change that you can get it removed. If you have a good payment history with the creditor who reported the late payment, try contacting them a negotiating for the late payment to be removed. If that doesn't work, you can try disputing it with the credit bureaus which forces the creditor to do a little extra work with the credit bureaus that they might not be willing to do in order to keep reporting the listing.

It can stay on up to 7 years, but if it is an isolated negative listing, it will probably only have an affect on your credit score for half that time.