The dog that took the burrito out of Anthony Stoner's (Tommy Chong) hand was not a trained dog, but a local stray. He simply walked into frame, took the burrito, and walked away. Cheech Marin and Tommy Chong ad-libbed around this, and it was left in the movie.
The team found it hard to get any of the traditional advertising outlets to promote their film so they hit on the novel (and ultimately successful) idea of putting comic strips on bus benches. This gave the film a certain "street" feel, helping it to become a cult hit.
The car that Tommy Chong drives at the beginning of the movie is actually owned by Jack Nicholson. When this movie came out one could buy fiberglass conversion kits to replace the trunk and hood lids to make them look like baby Rolls Royces.
Lou Adler screened the film privately for Jack Nicholson who had just been in a car accident and had a dislocated shoulder. It proved to be a painful experience for Nicholson, for his shoulder hurt him every time he laughed - which was often.
On the commentary track, Cheech Marin said that, while hanging out with Mike Judge, Judge revealed that his MTV series Beavis et Butt-Head (1993) was partially inspired by 'Up in Smoke.'