According to the DVD special features, the film was originally conceived as a vehicle for Cheech & Chong; Ivan Reitman has also stated that the reason this fell through was because their manager insisted (without the pair's knowledge) on a 25% share of Reitman's next five films, which he wasn't willing to give up. The script was then rewritten for Bill Murray and Harold Ramis, and most of the "stoner" humor was shifted to the "Elmo" character played by Judge Reinhold.
The last sentence the platoon shouts during their performance at graduation, "the quick brown fox jumps over the lazy dog", is a sentence that was popularly used to test typewriters and telegraph machines because it contains every letter of the alphabet at least once.
Before lights-out, Sgt. Hulka promises a 10-mile run in the morning. Then in the morning he says 5 miles, then ups it to 10 because of Winger's comment.
During the rescue toward the end of the movie, when a rocket is fired from the Urban Assault Vehicle toward a guard tower, a crew member is clearly visible crouching at the left of the scene attempting to conceal himself behind part of a building.
Traveling north from Italy to Germany, as Winger and Ziskey went with the RV to see their girlfriends, and their squad traveled in pursuit, one would have to take a RIGHT into the Czech Republic, and a LEFT into Germany, not a left into the Czech Republic and a right into Germany as the roadsigns falsely indicated.
What are the differences between the Theatrical Version and the Extended Cut?
A
The Extended Cut runs nearly 19 minutes longer and features seven additional scenes that do make the movie funnier and complete it nicely. This having said it's the version to get. A detailed comparison between both versions with pictures can be found here.