I got promoted to manager at the thrift store I was working at. Duties included training staff such as cashier's etc, as well as managers for other stores. Yes if someone did bad it did reflect poorly on me and that sucked.
I am a very emotional person and was also going to school full time while managing. There were many nights I came home crying because of different things that had happened. That is my downfall though and not everyone who gets that position is going to take things to heart the way I did.
There were also some super crappy things going on that sucked to deal with such as 2 of my cashier's scamming the store of money. While they were getting away with it my sales were down and that made me look bad, I was way too trusting.
I also had to do cash drops in the safe. One time 690 bucks came up missing, I believe I left it on the office desk during the changing of shifts when plenty of employee's were coming in and out of the office. That was 50 bucks out of my check until it was paid off.
Those are just some crappy things that happened. If you think that you can handle the responsibilities, and there are plenty of people who can I say go for it. Looks great on your resume.