Factual error: When Zach and Nomi are talking on stage after Nomi's disastrous experience at the boat convention, Zach places a call to Phil Newkirk. There are several problems with the call: the cell phone doesn't appear to be on (he raises the antenna at the beginning and end of the call, but he never presses an "on" or "off" button); Zach doesn't punch in enough numbers for the call to appear legitimate (too many numbers for speed dial, but too few for a local seven-digit phone number [also, since he was using a cell phone it's unlikely that he dialed a hotel extension number]); and the pauses between his words and Phil's response on the other end of the line are too short to be believable.
Deliberate mistake: When Cristal and Zach's limo pulls up in front of the Club Cheetah, the Stardust is prominently displayed in the background at a close distance to the club. In reality, the Cheetah is a popular and well-known strip club in Las Vegas. People such as myself who have actually been there know that when looking at the Cheetah from the angle seen in the film, there would be no possible way the Stardust could be in the background (in actuality, the I-15 highway would be in the background, not the strip).
Audio problem: When Nomi is dancing at the Crave Club with the bouncer, she kicks him for making a suggestive comment and the bouncer stumbles backward into another guy on the dance floor. The bouncer tells the guy to "be cool", and the guy responds with "you be cool, buddy", but as we hear him say this, he's already punching the bouncer and his lips aren't moving along with the words.