Take this MC piece for example...see how the drawers are inset into the dresser. This rubbing usually occurs simply because the piece is older and needs some tweaking.
I personally do not typically like to distress MC pieces. Glazing looks good sometimes and maybe if it HAS TO BE distressed or someone wants it I will, but as a general rule I think it looks better more modern.
Today I decided to take a few minutes and try to explain how to fix this issue very simply. I do have another technique I will share for more severe problems, but in a different post.
Hopefully you only run across minor issues and this particular trick helps!!
Here is an example of the drawer rubbing on the side...See how it's really tight and slightly touching the wood trim of the dresser. I planed/sanded this drawer down because it was not only rubbing but actually not shutting. (right drawer)
Here you can see that there is plenty of room on the right side of the drawer. Even after I sanded it down about 1/16" and it closed nicely, I knew that there would still be potential for this guy to rub on the side at times, no matter how much I took off. (Bottom right drawer)
This is where my hand dandy tacks come in! You will want to place this far enough back so that you can't see it when the drawer is shut but far enough up to catch the drawer just as it starts to potentially hit the side.
Get that tack in there really good with a hammer. See how the drawer is no longer rubbing on the side (we are looking at the bottom right drawer)
Here is an example of where the drawer is slightly touching at the bottom (drawer on top left with trim)
Put a tack close to the front but not so that you can see it when drawer is closed.
See, slightly raised and not touching or rubbing at all! I did have to take a tiny bit off the top of this drawer but totally worth it to make sure there would be no rubbing at all. (top left drawer)