Factual error: Chow is carrying around $21 million in gold bullion. A bar weighs 400 ounces. Gold prices at that time were around $1,200 per ounce, and he's got two bags, therefore he's supposedly carrying 8,750 troy ounces, or about 600lb/270kg, on each arm.
Continuity mistake: In the scene where Alan flirts with the store clerk, they share a lollipop. You can hear a "crunch" indicating that she chewed the lollipop. In the next shot, she takes the lollipop out of her mouth and it is still completely intact.
Continuity mistake: In the bar in Tijuana, when Chow stabs the knife into the table, we see the erect knife aligned with a green bowl located behind it, as well as four beer bottles grouped close together to the right of the green bowl. Then, the camera changes into another wide shot showing the view from the opposite side of the table; where we see that the knife is no longer aligned with the green bowl, it has moved closer to Phil, and the four beer bottles have also moved to different positions.
Continuity mistake: After his karaoke Chow puts his knife on the right side of Stu's neck, but for the rest of the movie we see the wound on the left side of it.
Plot hole: Chow emails Alan to meet him at a bus stop in Tijuana. That's all the email says and they manage to get to the right bus stop. It would seem rather unlikely they would just happen to get the exact bus stop Chow was going to given the fact that there would have been loads of bus stops in Tijuana anyway.