I would encourage her to find and fix her mistakes. Praise her for the effort and give her information as necessary, "If you put the heel on the bottom, they'll be more comfortable." Just today I told DD, "Thank you for picking out boots and putting them on. But they look a little funny. How about we trade them around so that your feet feel better today?" If I just said, "You put your boots on backwards" then she'd get upset, but if I tell her why, she seems to take that better.
You might also want to show her, at a time when you are not in a rush, how you know how your clothes go on. I've shown DD how to know her underwear is in the right direction, or what to look for so she knows it's not inside out. If you have her help you sort and fold laundry, then it can just be a conversation about clothes "Some clothes have fabric tags and some are just pressed on. Do you have more shirts like x or y?" vs her abilities.
You can also say, "Sometimes it's hard to know which way socks go, huh? Can you think of a way to remember? Should we mark a dot on the bottom?" Get her involved in a solution.
Or do a family "check" in a big mirror. "Everybody have a shirt? Pants? Socks? Are they in the right places? Are they right side out? Great! We're ready for school and work!"
I think that there are some things we need to catch at home to help our child avoid further embarrassment. Whatever you decide, I'd keep pointing it out and teaching her how to dress.