Continuity mistake: When Harold Ramis is fighting Bill Murray to try to keep him from leaving the base, notice when Harold is on top of Bill choking him, there is a duffel bag under Bill's head, and in the cut-aways the bag is a few feet away. (00:47:00 - 00:47:45)
Continuity mistake: When Harold Ramis pays off his pushup bet with Bill Murray, he throws the dollar bills onto Bill Murray's chest, and they move around and their number changes. (00:14:20)
Continuity mistake: When Bill Murray's girlfriend is leaving him for good, she puts her left boot on twice. (00:10:00)
Continuity mistake: When Harold Ramis is fighting Bill Murray to try to keep him from leaving the base, Murray's knit cap moves on and off his head during the scene. (00:47:00 - 00:47:45)
Continuity mistake: During the graduation scene, after the platoon arrives in front of the General's stand, Bill Murray begins running backwards. The shot changes to the girls in the stands laughing, and then back to the platoon. When it gets back to the platoon, you can see that Murray is once again just starting to run backwards.
Continuity mistake: When the platoon is escaping in the EM50, Sarge is on top and says, "I'm getting too old for this #%&*," he then lowers his head. The next shot, he lowers it again.
Continuity mistake: At the bus station, both MPs are wearing Specialist-5 rank on their uniforms. Later in the movie they seem to have been demoted to Specialist-4.
Continuity mistake: During the graduation scene, watch the band director closely when the music stops - you will see that his arms are still moving, as if he's conducting the band. (01:11:00)
Continuity mistake: When John drives the woman over the bridge in the cab, just before he stops the car there is a shot of the two occupants and behind the cab the bridge is deserted save for one red van. When the shot changes to an overhead and John stops the cab, the bridge behind them is crowded with traffic and the van is gone. (00:05:40)
Continuity mistake: When they are escaping from the prison camp, they knock over grungy, drab green 55 gal drums, which are nice and shiny inside. (01:37:30)
Continuity mistake: During the mud wrestling scene, a patch of mud alternately appears and disappears on the stomach of the woman in the white bikini.
Continuity mistake: When Bill Murray finishes the 5 pushups and wins the bet, in one shot there are 3 singles on his chest, in the next shot there are about 7, then back to 3. (00:11:30)
Continuity mistake: Oxberger's hair went from a super close buzz cut to much longer when they were introducing themselves, which would have been the same night, to close buzz cut, to longer. It's inconsistent throughout training. It's obvious the scenes were not filmed in order.
Continuity mistake: During the initial issue, Hulka's unit insignia appears, then disappears when he's talking to Bill Murray, depending on the camera angle.
Continuity mistake: At the Bus Station, Luise, MP, was a Spec 5. After that, she was a Spec 4. You can see it on the shoulder rank patch.
Continuity mistake: Early in the movie, the Sean Young character is a Specialist Five (Specialist symbol with one stripe over the top). At graduation and when she was getting off the plane at the end of the film, she was a Spec 4 (just the Specialist symbol).
Continuity mistake: When they're fighting and the two girls (MP's) drive up in the Jeep, you can see the shadow of one of the girls walking in front of the Jeep's headlights, but in the next shot they're just getting out of the Jeep.
Chosen answer: According to the movie's premise and plot, once they (the platoon) impressed the brass at graduation and was assigned to the Germany gig with the "EM-50", Sgt. Hulka would naturally be with them as he was their original commanding officer. Plus, it would be logical to suggest that he would personally assign himself the detail of overseeing his platoon as they were his to begin with.
CCARNI ★
He's assigned as a Drill Sergeant, that is his job. Once he was fully healed he would have been assigned another group of recruits.