It seems like the previous owner of my bike installed the rear brakes backward. I figured I could simply mount the brake on the other side. Unfortunately, this is not possible since the recessed nut only fits on the wrong side. I'm unsure if I should leave the brake backwards (as-is) or if I should enlarge the inner brake hole and mount it correctly. Although the curved washers should hold everything in place securely, I'm afraid the outer brake hole will leave some wiggle room. What do you think?
I believe they did it this way since it takes a right-angle drill otherwise.
The clean way to do this is just use a front recessed mount brake and install it non-recessed. In some cases one can also find and transplant pivot bolts to make this work. Here since the back side has now been drilled, it would be easy to imagine problems with the brake slipping around if the recessed nut wasn't where it is. Conceivably you could take up the space with something else, maybe an aluminum presta grommet, and then put a front on it. Unless the looks are really bothering you, leaving it is probably best.