At Heather Hills' Sweet 16 party, during LD's performance, Heather Hills swings at Rodrick with his mic stand, missing him, but in turn knocks her chocolate fountain over & away from her. In the next shot, she's seen standing next to her friend on the opposite side of the fountain, without the mic stand, & the chocolate fountain has been splattered onto her somehow.
When Rodrick hands Greg the remote control for the pyrotechnics at Heather Hills' birthday party, he is wearing a sleeveless shirt. In the next shot, he is wearing an over-shirt which he takes off to reveal the sleeveless shirt.
The goof items below may give away important plot points.
At the end, at Heather Hills' "Sweet 16," Rodrick sings. After Rodrick sings his song, Heather gets angry and swings one of the microphone stands towards Rodrick, who ducks so Heather hits the chocolate fountain. In the next shot, Heather is hit by the chocolate fountain and the microphone stand disappears.
Towards the end of the movie, Frank Heffley finds out that Greg was lying about his job, because the clerk said, "We don't hire minors." However, Holly Hills was hired as a tennis instructor (which is how Greg got his cover story in the first place) and the not-yet-16 Heather Hills was hired as a lifeguard.