Josh Peck's weight loss is mentioned when Helen tells Josh he can't be Santa because he lost so much weight.
This was shot the same week(s) that Miranda Cosgrove (Megan Parker) and Jerry Trainor (Crazy Steve) were shooting the Christmas special of a separate show ("iCarly").
The parents listen to a radio in their vacation hut. The same Packard-Bell AM Radio, Model AR-851 was used on Gilligan's Island (1964).
This movie takes place at least five weeks, but less than a year after "Really Big Shrimp". Helen's marriage is mentioned as being "recent", but she got sick of her new husband five weeks after the marriage. How soon after this came the divorce, and the events of the series, are unknown.
When Josh is arrested and has his mug shot taken, his registration number is NCC 1701, the registration number of the Enterprise in Star Trek (1966).