On the plane, when Barney and Vinnie are flying to New York, Vinnie is paying the stewardess for his alcoholic drinks. When he raises his left hand, to pay the stewardess, he is handcuffed to Barney's right hand. A few seconds later he is telling Barney about his tipping "philosophy". He asks Barney for a pen and Barney raises his right hand, which is no longer handcuffed to Vinnie's left hand. Then, a minute later they get off the plane and are handcuffed together again.
When the new park for the home town "Turtles" opens, the first ad sign on the right field wall says "Go Lions!"
When the family and Vinnie go to the baseball game, they clearly sit behind a row of seats (with fans in them). The following shots of them singing the National Anthem has them sitting behind a railing, not behind a row of seats with spectators.
When Vinnie and his wife first drive up to their new house the mail box flag is up. A few moments later the flag is down.
The turtle is first shown in a glass dish with two handles. When Mrs. Stubbs goes to wash the dish, it has no handles.
The Witness Security Program is under the jurisdiction of the Marshals Service, not the FBI.
Throwing out the first pitch of a ball game occurs from the pitcher's mound to the catcher, behind home plate. Vinnie throws out the first pitch from the 3rd base line to the pitcher's mound.
The FBI agent asking Vinnie for his social insurance number would have never happened because the Witness Protection Program would have provided him a new one.
(Possibly deliberate errors by film makers): The FBI would not send Vinnie to live in a town/city where there are other mobsters in the Witness Protection Program. Vinnie's reunion and subsequent crime spree with his old pals would be the very reason why they would avoid placing in a city with other mobsters.
Rick Moranis's partner is playing a video game on a Nintendo Entertainment System but the sound effects are from the Atari 2600 version of PacMan.
Stuntman visible when Vinnie jumps behind stacks of wood at the ballpark during the Christmas anecdote. He is visible in the bottom as Vinnie stands up with a gun.
Close-ups of photographs in the Stubbs house show the family wearing the same wardrobe as they are in the scene they appear in.
At the end of the movie, when it is one year later, Vinnie and Crystal have a baby girl. The girl is at least six months old. The oldest she could have possibly been was three months old.
When Vincent tells Hannah his old dog's name, the audio says, "Fangool" but his mouth says something else.
In the motel room, Kirby plays "The Goonies II" on a Nintendo Entertainment System, but the audio is clearly from "Pac Man" from Atari 2600.
During the first dance sequence (when Vinnie teaches Barney how to dance) the song played features a brass section, yet the band does not have one.
Reflected in Vinny's sunglasses at the start of the movie.
Fryburg Police officers are wearing Los Angeles Police Department Badges (Los Angeles City Hall is featured on LAPD Badges).
When Barney spends the night with Hanna, she explains that the kids are not home, thus keeping their budding romance secret from her kids. The next morning Hanna's ex-husband barges in to the house expecting the kids to be ready to go. Both Barney & Hanna appear to just be getting up in the morning, and could not have kept up the ruse had the kids been present or just returning from her mother's. The ex-husband is expecting the kids to be ready to go, and their absence would be a serious breach of a joint custody arrangement - especially for Assistant District Attorney Hanna.
After Vinnie marries Shaldeen in Reno, he is talking on the phone with Barney - and then puts Shaldeen on the phone to speak with Barney. When they're done, Barney asks Shaldeen to put "Vinnie" back on the phone. Shaldeen knows him as "Todd" not "Vinnie."
When Barney tells Vinnie "Keep your nose clean, capisce?" and mispronounces "capisce" as "capisse," Vinnie corrects him, pronouncing it "capeesh." The correct pronunciation is "capeeshay." "Capeesh" is how the word is pronounced in an Italian (slang-like) dialect. Although Vinnie could be using the alternate pronunciation, this would be inconsistent with the scene where he meets his mother and speaks fully articulate Italian with her.