At Moroni's hearing, you see assistant DA Tommy Kelly wearing a wedding band, yet he hasn't married Sally yet.
When Johnny says he joined the Jocko Dundee Gang full time there is a picture of him and the gang with Vermin, but Vermin doesn't join the gang until two scenes later.
Before the explosion in Dundee's bathroom, the parrot is shown on the left side of the perch. In the next shot showing the parrot flapping its wings in reaction to the explosion, the parrot is on the far right side of the perch.
Johnny's hair changes length when the Moronie robot arrives.
Danny Vermin has a (fictional) .88 Magnum revolver, which features an unusually long barrel. Caliber refers to a bullet's diameter, so the barrel should also be unusually thick.
The name of Richard Dmitri's character is spelled Moronie on his club sign and in newspapers. In the credits its spelled Maroni.
When Ma Kelly pours whiskey from her fake camera during the graduation ceremony, she only fills Johnny and Tommy's shot glasses, but not hers or Sally's. Yet, when they toast, all four of them raise their glasses to drink.
When assistant D.A. Tommy Kelly goes to the D.A.'s mansion to tell him he has enough evidence to convict Johnny Dangerously, he says he has, among other things, recordings, and he holds up a reel of audio tape. This scene is set in the 1930s, but magnetic tape wasn't invented until the late 1940s.
At the end of the movie, Tommy Kelly sees The Roaring Twenties (1939). The latest date in this movie (the year it was being narrated in) is 1935.
During the chase scene after Johnny escapes prison Alan Hale's desk sergeant character is giving updates during the chase. He is reading the information from tractor-fed paper from a dot-matrix type printer (notice the pin holes along both sides of the paper), which wasn't around in the 1930's. It wasn't widely used until the 1960's.
In the educational film that Johnny shows his brother Helvetica typeface is used. The Helvetica typeface was not created until the 1950s.
When Johnny is trying to get into the club after being dropped off by Lil, he ducks behind a white car. The poster on the cinema behind him is playing "Jack London's, Call Of The Wild" with Clark Gable. This movie was released in 1935, where as the scene is set in the very early 30's.
Vermin supposedly found out that Johnny Dangerously's real last name is Kelly after Tommy gets married. However, Vermin and Johnny knew each other as kids, so Vermin would have known what his last name was already.