When Hawkeye is doing some filing, Sgt. Vickers comes in with paperwork for two re-enlistees. As Hawkeye reads the forms he sees that one re-enlistee is Klinger and looks up at Vickers. But in the next shot Hawkeye is still looking down at the forms.
During the epilogue, Klinger takes the 45 record out of the jukebox (that was playing his and his ex-wife's song) and smashes it on the jukebox. The sound it makes is of a porcelain dish breaking, not a vinyl record.
Klinger, speaking to Col. Potter, quotes the author Tom Wolfe: "You can't go home again." He mistakenly attributes this to the fictional character Nero Wolfe, created by mystery writer Rex Stout.
At the end, when the camp is honoring a nurse/private, Klinger rides up on a horse and is said to be naked. However, when a close up is shown, you can see that he's wearing skin colored shorts under the white fake hair.
When Col Potter is giving Hawkeye and the rest of the officers the pep talk about how good the Army is, the shadow of the mic is visible behind Father Mulcahy.