Continuity mistake: When Spongebob and Patrick approach the county line, they meet the two laughing fish; one is short and fat, one tall, thin and has two patches on his knees. These patches disappear in one shot; when the short fat one is bouncing on the other one's stomach and they're both laughing.
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Continuity mistake: After Spongebob and Patrick receive their "seaweed mustaches" they jump off the edge of the trench. When they figure out that they just jumped off the edge they look down, and directly below, the trench wall is visible with nothing on it. Yet, when they are about to hit the ground there is a branch.
Continuity mistake: When the boys drive up to the gas station, the guys in the rocking chairs start a conversation with them. The guys' last words are "You boys won't last 5 seconds over the county line." The boys drive about five feet over the county line, and some guy steals the Patty Wagon. When the boys ask the guys how long it took, you can see that they are closer to the county line than before.
Continuity mistake: During the 'Goofy Goober' test at the Thug Tug, the gang leader says "DJ, time for the test!" We see he has a blue hat and glasses before he puts the record on. Later, the gang leader says "DJ! Turn it up louder!" we see that the DJ now has a red/orange hat.