Continuity mistake: When Chong's father is shouting "we're not gonna have a family brawl," there is a big bottle of juice on the edge of the table by Chong. It cuts away for three seconds and then back to Chong. The bottle of juice has moved to the middle of the table. Also, Chong has poured juice into the mixture. He wouldn't have had time to do all that in just three seconds.
Revealing mistake: When the cop on the motorcycle pulls Cheech and Chong over, one of the hippie girls is sitting in the front with Chong. Chong orders her to get in the back. She goes back behind the curtains and sticks her head out front. He pushes her back again. In a shot from the back of the van, you see Chong pushing her back, but you also see through the crack in the curtain that it is totally dark in front of the van. Since there is daylight outside, it shouldn't be totally dark.
Continuity mistake: After Cheech has asked the girls if they need a ride he spots Chong hitchhiking. He then takes a u-turn to the other side of the road. At this time you still see the girls sitting in their original position. When it cuts you suddenly see a van has appeared from out of nowhere and the girls are suddenly walking to it.
Visible crew/equipment: When Cheech and Chong get to the border, Cheech spots some nuns in the car beside them. Watch closely in the window of the van when Cheech is looking at the nuns. You can see a man standing there looking at something and then looking at the van. This man wasn't standing there when there was a wide shot of the scenery.
Continuity mistake: The drum kit is a Ludwig amber Vistalite (see Keith Moon, who had a clear one, and Karen Carpenter, a blue one, neither had bottom heads) like John Bonham played in the Song Remains the same. The drum head on the kick drum in the back seat is on and off in the same scene repeatedly. They're a pain to remove, so it's physically impossible to do so and replace in the same conversation.