While Sophie is speaking to Stan in the bar after discovering he is an FBI agent, her belt goes from being outside her jacket to inside her jacket between shots.
When Agent Lloyd is first trapped in the Suburban and Max is reversing it into the vehicle behind it, there is raised white lettering on the tires of Lloyd's Suburban. Just minutes later, when the Suburban is getting pushed off the street by the semi, the tires have changed to plain blackwalls with no white lettering.
When Stan's car is being commandeered, the airbag is deployed and covers Stan; however, in the immediate following cuts, the airbag is not visible. Once the car stops, you see a deflated airbag.
When Stan and Max are drunk and getting off the fishing boat, Sophie's gun in on her left side. After chasing the intruder off of the cruise ship, her gun is back on her right side.
When Max is 'gassing' Stan in the Suburban, he connects the gas to the AC refrigerant system which is a closed system. It would be impossible for the gas to get into the air vents.
When the American FBI agents surprise Max and Stan in Stan's hotel suite, the gunshot scar on Max's left shoulder has disappeared.
When Stan is rushing past the ship's lobby to accost the stranger in the hazmat suit, he runs over two black electrical cables draped across the floor. Known as "stingers", these cables likely go to one or more lights that were hastily added to the set in order to light this quick shot.
Around the 11 minute mark the shots of two sailboats moving across the scene is taken at Lanikai Beach on Oahu Hawaii. They're supposed to be on some Caribbean island.
During the opening heist, Stan is delivering the diamond to the museum which is actually the unmistakable Frank Gehry designed Walt & Lillian Disney Concert Hall. The sun is shining west across Grand Ave. meaning the basketball game is happening during the early morning. Also, Max seems to "teleport" from the Staples Center (or whatever it's being called when you read this) at Figueroa and 11th to a rooftop overlooking the Disney at Grand and 1st.