The extra (wearing a striped shirt) behind the limo driver at the airport is not using coins while supposedly playing the slot machine (he is, apparently, an unauthorized extra that snuck onto the set).
Ellen leaves Wayne's mansion in complete disgust after he offers her a lock of his hair. However in the very next scene, she shows up at the casino wearing a Wayne Newton outfit and can't stop talking about him.
When the fake ID salesman takes Rusty's picture, Rusty is smiling. Later, when we see the ID card, Rusty isn't smiling in the picture. Also, when the picture was taken, there was no background other than the Vegas city lights. When we see the card, there is a blue background.
In the opening scene as Clark swerves wildly around the neighborhood, he almost hits a group of kids who jump out of the way. However at the same time, you hear a kid joyfully express a "Hey Mr. Griswold!".
When Clark plays three hands of Blackjack at once, the overhead shot shows him being dealt three hands. however, in the next shot, when Eddie has the waitress light his drink on fire, there are no cards on the table.
When the Griswolds get ready to leave Eddie's place for Hoover Dam, Eddie gets the babysitter (the box of snakes) and yells, "Hey kids...it's round-up time." When the snakes are on the ground, you see Eddie's hands below his waist, not holding anything. In the next shot, Eddie throws an empty box over his left shoulder and says, "Where we going?"
When Clark is using bubble gum to seal the leaks in the underground tunnel he sticks a piece of chewed gum on a piece of gum that is being inflated by water. It then cuts to Clark attempting to seal another leak and then back again and when it cuts back, there is no piece of chewed gum on the bubble.
When Clark, Ellen, Rusty enter the dance club to look for Audrey, when you see a view of Cousin Vicky, a couple walking behind her in front of the bar skip further ahead, although a shot of her is continuous.
At the buffet with Eddie and his litter,Clark and Eddie are at the buffet line when the pompous cook can be seen swapping the signs while he is talking and again when the camera pushes in on the yellow and blue goop.
The club Vicki is a dancer at has an address on Las Vegas Blvd (AKA The Strip) according to the taxi cab ads. However, when they emerge from the club, they are standing across the street from the Hard Rock Cafe. There was only one Hard Rock Cafe in Las Vegas in 1996/1997, and it is at the intersection of Paradise/Harmon, which is actually about a mile east of Las Vegas Blvd.
The road the family members are seen driving down at the end of the film is Interstate 15, which would take them to California, completely the opposite direction of Chicago, as the superimposed road sign states. (On an unrelated note, if they had continued going down this road, they would eventually get to Baker, California, which is the site of the "World Largest Thermometer" mentioned by Audrey earlier in the film.)
The family drives from their hotel, the Mirage on Las Vegas Blvd., to Cousin Eddie's trailer in Jean, which is south of Las Vegas, yet some of the shots of the family supposedly driving to Jean show the road that goes through Red Rock Canyon. You would not drive through Red Rock Canyon to get to Jean; Jean is directly south of Las Vegas, and one would simply drive south on Las Vegas Blvd. to get there. Furthermore, the drive seems to alternate between shots of Red Rock Canyon, and the actual Las Vegas Blvd. path that leads to Jean. Red Rock is west of Las Vegas proper, and one would have to go far out of their way to drive down this path. (On an unrelated note, during the "Hey, Girl" scene with Audrey in the back of the truck with Vickie, they are heading north on Las Vegas Blvd. towards The Strip; THIS is the road someone would use going between Jean and The Strip.)
The Griswolds emerge from the dance club where Vickie works, and are across the street from the Hard Rock Cafe. This would place them squarely at the intersection of Paradise/Harmon, roughly a mile or so east of Las Vegas Blvd., where the MGM Grand is located. Yet the film implies they simply walk there quickly. Going by foot, even if they were hurrying, this is a walk that probably would have taken nearly an hour. They could not have taken a cab because they had no money.
On the multiple occasions that Marty revealed a Blackjack (21) with the ace being the visible card, he hadn't offered Clark insurance, which is what a dealer is supposed do do when they are showing an ace.
In the very beginning of the movie (over the opening credits), a Chicago radio station is heard playing while Clark is driving home. The call letters are KLITE(pronounced on the radio as K-Light).
There never was a Chicago radio station with those call letters. In fact, radio stations east of the Mississippi river start with "W". West of the Mississippi they start with "K".
When The Griswalds are playing Keno near the end, only ten numbers were called. Regardless of how many numbers a player picks or is allowed to, 20 numbers are always called in Keno. As it is played in the movie, the odds of winning this game would be astronomically worse than winning the lottery.
When the Griswolds are shown on the airplane en route to Las Vegas, there are seats in the middle of the plane's cabin, rather than simply a few on the left and a few on the right. Wide bodied aircraft like this are typically used for much longer flights than the one from Chicago to Las Vegas.
When Clark is shooting craps and he gets a 7 on the Come Out Roll, the Base Dealer nearest to Clark calls the number. That is the job of the stickperson. The Base Dealer near Clark is not even supposed to be looking at the other end of the table when the dice are thrown.
When Clark says they never knew the man's name who gave them the Keno ticket, the paramedics said Mr. Ellis. However, due to HIPAA regulations, it is illegal for health care workers to disclose confidential personal information. They could lose their jobs and/or pay a fine.
When the family arrives at the Hoover Dam, Cousin Catherine says she loves electricity, and that Eddie has said they will get it soon. However, earlier in the film when Ellen and Catherine were in the kitchenette of the trailer, Ellen opens the fridge door, and the light is on, so it is powered. Perhaps by a generator, but it's still electricity.
When Clark is standing outside the lavatory doors on the plane prior to attempting to "join the mile high club", there are clearly only a few inches between the three doors. When he finally steps inside the center lavatory with Ellen, there is obviously at least a foot between the edge of the door and the wall.