There's a dozen threads about the clasp. Grab 600grit or an emery board and knock the edges off. Got it. That fix makes sense, but sanding off a lip on the bracelet is different than the case, imo. I also worry that the other nearby edges and finishes will be damaged fixing this myself.

Is this edge sharp only on my watch? It's only on this side, in this area. It doesn't carry onto the lugs. Can you check yours and see if it's remarkably sharp?

It's not dangerous because it's such a shallow edge that it cannot catch on skin or my normal shirt cuffs - BUT it is as sharp as any machined edges can be.

 

Nothing noticable on mine?

 

The caseback of my new Speedmaster FOIS was also extremely sharp, so sharp that it would even leave microscratches on my wrist. And i had some skin irritation. I was thinking about swapping the caseback against a flat saphire or so.
I brought it to the AD and the watchmaker solved the problem. He took off the caseback, taped it around and softened the edge, but so that you would not see any difference visually, but you do feel the difference when you go over the edge with a finger. Since then no problems. But its not the most comfortable caseback nevertheless..

 

It's something to FEEL between where I've put arrows on my pic.

 

Mine is not sharp or unpleasant.

 

Wear on NATO?
I never found it an issue.

 

It's on a NATO...

MY issue is on the case, per my picture - not the case back. Eve's case back post explains how a watchmaker fixed it.