2001: A Space Odyssey - When Chatty says she can't let Timmy turn her off and displays a red dot "eye", she is referencing Hal 9000's quote.
Keyboard Cat - Chatty shows Timmy a video about a cat playing the piano which is a reference to the famous internet meme.
Apple - Timmy's addiction to Chatty could be a reference to today's kids addiction with iPhones.
Chatty might be a reference to Siri, a voice automated personal assistant for Apple products.
WhatsApp - The way the kids get hooked to their smartphones when chatting could be a shoutout and/or similar case to actual WhatsApp usage.
Timmy's new cell phone is green on the title card and grey in the episode.
When they were at the Time Before Fun Museum after Chatty turned into a monster, the first time zoomed out there was only 1 switch. When it was zoomed in there were 2 switches.
The ending credits for this episode credit Jim Ward and Grey DeLisle erroneously for each other's characters.
In this episode, Cosmo said his favorite color is bleach. But in Where's the Wand? and other episodes, he said his favorite color is green, although he may like both (Look at Where's the Wand? for the same goof).
When Sparky squashes the accelerator, the accelerator's form is a dog's paw print even though it is Mr. Turner's car.
On the title card, Timmy's phone has a gold crown on the bottom of it. But in the actual episode, the crown is grey.
When Timmy pulls the lever, the words "Bed Zone" isn't on it. Then, when Wanda says, "Wrong lever, sport!" the words "Bed Zone" is on the lever.
When Mr. Crocker presses "Gloat Mode" on his phone, there is only one bar. However, it is the biggest bar, not the smallest bar as it should be.