I watched it, too. Found a scene where Hanks is talking with his squad and his Thompson is slung on his back muzzle up...the next scene seconds later shows the Thompson slung across his chest muzzle down.
Anyway, despite the nit-picking, I've yet to watch the Normandy graveyard scene where Ryan asks his wife to tell him he's led a 'good life' and not get a painful lump in my throat and tears in my eyes.