In these two episodes, Timmy is seen wearing a neck brace.
It's worth noting that this is the only episode where Timmy's Dad actually seems to like The Dinklebergs in contrast to most other episodes where he hates them. This may be due to their lack of adult friends in this episode.
Twister - The game Mr. and Mrs. Turner wants to play with their neighbors "Twisty" is a spoof of Twister.
Olive Garden - The restaurant where Cosmo, Wanda and the Turners were eating "The Gilded Lily" have some similar aspects from the Olive Garden.
Timmy - "Do you expect me to let you get away with this?", Vicky - "No twerp, I expect you to cry!" - This quote is a reference to the scene from the 1964 James Bond movie, Goldfinger, in which Bond says to the titlular villain "Do you expect me to talk?" where Auric Goldfinger replies to Bond "No, Mr. Bond, I expect you to die!" In both instances, a laser was about to cut the main protagonist.
Friday the 13th - When Timmy' parents, Cosmo and Wanda were in space, Vicky was wearing a hocky mask and using a saw, which makes a reference to Jason Voorhees, the main antagonist.
The Vikings brandishing their swords at Timmy's parents when they think Timmy is being threatened by them and Timmy has to tell them to not do it and why not to. And they are forced to withdraw back their weapons.
The neighbors being afraid of Timmy's parents and retreating away from them when they offer to spend their day with them.
In the title card, Mrs. Turner is wearing a pink shirt rather than purple.
Chester entered the house two times: first through the chimney, and then through the toilet.
It is unknown how Timmy's parents can have cell phone connection on the moon since there is nothing there that will transmit what they are saying to Timmy.