I agree with some of the above for sure. Knowing the manufacturing end will help you not sound stupid with your suggestions and knowing that real management buy in is invaluable.
I think the thing I learned the most is how to work with the operators. It's a constant battle. If you want to put out something they are doing wrong sandwich it into a few good things to soften the blow and make it look like your not always being negative. You want to be "friends" with them because they are the ones who are really going to make or break your food safety system. Don't be the quality cop unless you have to.
My latest lessons have been not stepping on other managers toes... that one bit me recently but I'm new to being a manager and he's retiring in a few months so it won't haunt me forever.