Its the scene where Matthew McConaughey is talking to Bill Paxton on board the decoy sub. McConaughey enters the captains quarters inquiring why he didn't get a recommendation. When Paxton looks up and the shot changes look at his bunk the lettering U.S. Navy is backwards on his blanket.
You're right, I noticed this too, because I couldn't read what it said, after watching the movie again, I noticed that it DID say U.S. Navy backwards. This could be a slip-up, or it could just be that's how they folded bed sheets? I don't know. I'm not saying I disagree with you, I'm just saying that it could be a possibility. Good eye though!
im not sure what the lettering looks like (stiched or painted on) but i suppose that if it is sewn in than the other side of the stiching would be backwards. same with being painted/printed on it. the other side of the blanket woul;d have it backwards. so maybe the blanket was laying facedown. just a thought. im going to have to check this one out.