Definitely tell her in advance. Taking minutes can be really hard to keep all the details straight. Frankly, in most organizations I'm involved, it's pretty common for the secretary to have the President or another officer proof the minutes before the draft is presented to the group.
Just be very positive about her work and matter of fact about the changes.
Note - if you are working electronically (in Word), investigate the feature "track changes". It's a little weird at first but gives you the ability to see each other's edits. If you simply make the changes for her, she won't have an opportunity to learn. Frankly, it might be easier to give her a marked up paper copy.
I would correct the mistakes on the copy she gave me, give them back to her and very nicely tell her that I noticed some errors and thought she might want to double check her notes and make corrections before she submits the minutes for approval at the meeting.
I never thought much about minutes until last year when we had some very big issues and had to refer back to our minutes to verify what was said and decided at some previous meetings. Our secretary's organization was a godsend.
I just received the minutes from our first meeting of this year (taken by a new treasurer) and there are some errors. It's stuff like misspelled names, issues listed under new business when they were actually discussed under old business, an event mentioned in the minutes when we didn't actually discuss it until a week or so after the meeting, etc. Not sure what I should do. Should I correct them and send them back to the sec? Wait until the reading of them at the next meeting and correct them then? Or just let it go. I don't want to be picky we're all new here but I do want an accurate record of the meeting. Any advice?