The "Pig in a Poke" host asks the Griswalds about the leader of the 1804 American Expedition, leading them with "What Lieutenant lead that expedition?" Ellen Griswald inadvertently answers by saying Clark's name. The actual answer is "Lewis," who was a Captain. William Clark was also a Captain, but Meriwether Lewis was the leader, and Clark was a follower.
When Clark and Ellen are in the club watching the topless dancers, and Ellen notices Rusty with the hooker, she tells Clark to "Look who she's with". As he turns to Rusty and the camera shows Rusty with the hooker, the hooker's blouse slips off her shoulder, temporarily exposing her breast. It is obvious this was not scripted, and she immediately covers up.
When the Griswalds are getting their picture taken in front of the fountain, as Clark is showing the thief how to use the camera, the thief's shirt has bunched up at the bottom. You can see Clark straighten his shirt as he moves around to the front of him.
The first time the Griswalds drive their yellow Austin Maxi, Clark drives on the wrong side of the road and hits another car. The yellow Maxi's left front fender is badly damaged. In subsequent shots, the damage is much less severe.
When Clark mixes up the English hotel rooms, the door on the left leads to the lobby; the one on the right leads to the strange woman. After he meets the strange woman, he runs out and meets Ellen in the hallway, but he emerges from the lobby door, not the strange woman's door.
In the Paris hotel room, Clark flops onto the bed and falls off. He quickly gets up and sits on the side when Rusty appears to talk about acclimating to France. Suddenly out of nowhere, Clark produces a set of berets from behind him for the family to wear.
Rusty suggests the family go to the top of the Eiffel Tower. When the Griswalds are at the tower, the down arrow in the background means they are clearly on either the second or first level. The elevator is the only way to the top, and the observation deck is not that big.
During Ellen's dream on the plane of the Queen's reception the guests are greeting the Queen, Princess Diana, and Prince Charles and then turning away. You always face the Queen and never turn your back to Royalty in Great Britain. This is probably deliberate to show how uncultured the Griswalds are.
Clark calls the street in Germany "Dipplestrabe" with a B sound. In reality, the German character which looks something like a B, represents a sound like "sz". This is almost certainly deliberate, to show that Clark is an ignoramus.
When Ellen talks to the crook in the dining room, she says she used the F-word in front of the kids. In the R-rated theatrical release, Ellen screams "Fuck!" when she sees a billboard advertising her "movie". That shot was removed from the home video version to make it more appealing to a family audience.