How common is it for submitted papers to have minor errors?
That's what peer review is there for: to tell the author about the minor, but correctable mistakes in the paper. 

The way I see it is that, of course, I spend a lot of time writing my papers and making sure that everything is correct. But pragmatically, you will have to come to terms with the fact that no paper will ever be perfect. There comes a point where you just have to take the plunge, submit it, and hope for the best.