Continuity mistake: Since the beginning Jules had a cherry red Lexus car. The car she drove into the pool was a random blue one never seen in previous episodes and immediately afterwards her red car reappeared when driving with Ellie.
A Mind with a Heart of Its Own - S3-E2
Continuity mistake: When Jules suddenly appears on the roof she is wearing red flip-flops. When we see her feet again she is wearing black strappy sandals. When she stands up she is barefoot. When she travels down the zipline she is wearing the black sandals again. (00:15:20)
The Trip to Pirate's Cove - S5-E4
Visible crew/equipment: While Jules watches Ellie do her charming-Ellie thing, Jules says, "Shiver me timbers, who is that," and right at the start of the next shot as Chellie talks about her seamstress, the red T-mark is visible at the bottom of the screen beside Ellie's chair leg (where Jules will stand in a moment). (00:06:15)