When Derek finishes talking to Matilda on the Walkie Talkie in Maury's office he turned "left" to go back to helping Hansel look for the computer files. A large premise of the movie is that Zoolander is unable to turn "left".
When Hansel is telling Derek about falling off a mountain he says "Hansel haven't you been smoking peyote for 6 straight days couldn't some of this be in your mind?". But the thing is you can't smoke peyote you can only ingest it.
When Mugatu is explaining to Derek why he wants him to campaign for him, Todd brings him a large coffee. Mugatu spits it out, with no foam mustache, and for a second a foam mustache appears. After Derek's surprised look, it disappears again.
When Derek is looking in the puddle after the male model of the year awards, he gets splashed by a passing vehicle and has mud on his face. In the next scene when Hansel is riding by on his scooter, Derek's face is clean, as if never being splashed by the mud.
Almost at the end of the movie when Derek is about to leave Maury's office he hands his phone to Hansel for him to give it to Matilda. Hansel already has the phone in his hand and says "Ahh man!" but in the next take Derek gives him the phone again.
The shots of the rallies in Malaysia seem to show banners displaying Chinese text, while the Prime Minister's platform shows English and Arabic text. All of these are highly unlikely in the real Malaysia itself. The national and dominant political language of Malaysia is Malay, and is written in Romanized text due to Malaysia's past as a British colony.
When Derek is being interviewed before the Male Model of the Year Awards, the flashes of the photographers can be seen reflecting off the background/other people, yet when the camera *shows* the photographers with their cameras, the flashes of light do not come from the cameras themselves, but rather from above.