Revealing mistake: When Bill Murray and Harold Ramis are whipped into the rope snare traps there are huge gaps in the ropes between Harold Ramis' feet that would make it impossible for the trap to secure him.
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.
Other mistake: In the private conversation scene with Bill Murray and "Sarge" in the latrine at basic (Sarge's office) the toilet bowl in the back left corner is installed backwards. (00:43:03 - 00:45:10)
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)
Other mistake: During the graduation scene, if you watch as the platoons are marching by, you can see that several members are not in cadence as they should be. This also includes the men walking between the platoons that are supposed to be setting the cadence and they are out of step with the platoon in front and behind them.
Factual error: SFC Hulka was assigned as a Drill Sergeant and is therefore authorized for the Drill Sergeant ID badge which may be worn for the duration of his career. It is missing from his dress uniform in Europe.
Factual error: During basic training, civilian clothes are locked up in a storage room; therefore, none of the troops would have access to them.
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).
Factual error: It is highly unlikely that junior enlistees would have clearance or access to a TOP SECRET manual for the Urban Assault Vehicle. Also, the manual shows "WAR DEPARTMENT" on the cover. The correct name since 1947 was the Department of Defense.
Factual error: The German license plate on the car parked at the "Schloss Hotel" starts with the letters "WH." This was reserved for Nazi Wehrmacht Herr (Army) vehicles and was discontinued in 1945. In addition, there is no hyphen (Bindestrich) separating the letters from the numbers. There is also no circular inspection / tax stamp sticker on the plate.
Revealing mistake: The couple make love in the General's bedroom in the US. Later they make love in a German hotel room. The same set is used for both scenes.
Factual error: Stillman's aide is wearing his hat indoors. Soldiers do not wear head gear indoors unless they are armed.
Factual error: Francis "Psycho" points a knife at Winger. Weapons of any kind are absolutely prohibited in basic training. Granted he could've smuggled it in, but it most likely wouldn't make it past the shakedown part when arriving at basic. The Army and Marines prohibit weapons of any kind in basic training.
Factual error: A couple of issues with military awards as seen in the film: First, Sergeant Hulka is wearing the WWII Victory Medal, which he would not be eligible for according to his self-stated time in service (28 years, making his date of enlistment sometime in the early 1950s since the film is set in the early 1980s). Second, Captain Stillman wears the United Nations Service Medal for Korea, even though he is obviously far too young to have fought in the Korean War. (01:15:43)
Factual error: The mortar round which injures Sergeant Hulka isn't realistic. If it was a training round, its explosive would not have been sufficient to knock down the tower (based on where it lands - near the base of the tower) ; if it was an actual high explosive round, everyone within a 25-meter radius (basically all the recruits) would have been killed or seriously wounded by shrapnel.
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.