Factual error: During Globo Gym's commercial at the start of the movie, White shows a picture of himself as an obese man in 1987 and indicates that was him 6 years prior. However in the same commercial, you can see a woman grab a bottle of Vitamin Water from a likewise branded fridge. Vitamin Water did not exist in 1993. In fact, its parent company Glaceau was not founded until 1996.
Continuity mistake: When the six main characters are watching the movie on how to play dodgeball, a young Patches messes the little boy's hair, leaving it sticking up in the back and mildly flat in the front. In the very next shot, the little boy's hair is neat and all flat. (00:23:50)
Continuity mistake: During the tournament when it's just Gordon versus the entire other team, the background advertisements change multiple times. The problem is, they appear to be hung there, not electronic.
Other mistake: Peter took the $100,000 bribe White gave him and turned it into $5,000,000 by betting on his team. He did this, so he could buy enough shares of Global Gym stock and take over the company, and in the process kick out White as the CEO. The problem is $5 million wouldn't be near enough to gain control of the company, to be public its value would have to be at least in the tens of millions.
Chosen answer: "Deus Ex Machina" means "God out of the machine." It's from Greek plays, wherein a god would appear at the end of the story to solve a problem. Nowadays it basically means that a totally new plot element appears out of nowhere and solves everything. It's an easy (and cheap) way out.