When Peter is in the camping store with his parents and walks away to think about whether to accept the lantern his parents want to buy him, the lantern's handle is up/down/up between shots.
The collection of flowers are not the same when Mike first brings them home to the time they make it to the dining room table. For example, there are gladiolas when on the dinner table, and no gladiolas when Mike first brings them home.
When the vase first starts to leak, Greg places his finger on it to stop the water from spilling out. In the next shot of the vase, his hand is not there.
At 8:21 when Greg is filling the vase the water stream is seen twice to almost shut off before he even touches the handle.
When the vase is first broken by Peter, it only breaks into three pieces. In the tag scene where Carol asks Peter to "Glue the vase back together, and this time, do a better job," she drops the vase and it breaks into many pieces. Therefore, it is a different vase. Looking closely at the vase in the tag scene, it is clearly a different color than the one that was broken originally.
During the dinner scene when the vase starts to leak, there's a shot where you can clearly see the water hoses under the table (feeding the vase), and you can see plastic covering the floor.
In the next close-up shot of the broken vase on the floor, you can see the shadow of a crew member's foot on the top-left of the screen.