At the part when Captain Steele catches the soldier making fun of him in front of his friends, listen, Captain steele says, " I'd like a word with you, Specialist." Now, the soldier he's talking to is Dominic Pilla, who has the rank of Sergeant! Still a good movie though.
Often the military (or at least the Marines) will "reduce" a guy to show he is in trouble, for example, a SSGT made be told, "Sgt, go see the 1st Sgt, and, CPL, when you get there, tell him, LCPL, why you said :XXXX:, understand PFC?"
I belive that was the intent here; I also noticed it
In the scene, after the commander catches the soldier making fun of him, he calls him "Specialist" in jest, as a playful warning to what could happen if his behavior continues, because Specialist would be one rank below Sergeant. It's a common thing to do in the military.
Actually, this is not a slip up at all, but historically accurate. Specialist Pilla was promted to Sergeant the day of the mission. Look here for more information on Sergeant Pilla-http://www.nightstalkers.com/tfranger/memorial/pilla/default.html