There is not always a bathroom in Timmy's bedroom.
While drinking a slushy, Cosmo claims he can't get brain freeze, thus proving he has no brain. However, in a previous episode while disguised as pistachio ice cream, Cosmo licked himself and turned blue with brain freeze.
Poof learns to talk on three different occasions throughout the series as if he had never done it before.
Behind the scenes, there is no floor plan for Timmy's house. This gives the artists the freedom to draw certain rooms slightly different each time. It also creates multiple continuity errors about where each room in the house is located, where the items and furniture in each room are located and which window belongs to each room from the outside of the house.
In the Pilot episode Timmy receives Cosmo and Wanda during the first night he gets babysat by Vicky. But in the movie "Abra Catastrophe" it's revealed that Timmy was babysat by Vicky for 2 years before he received Cosmo and Wanda.
When Timmy wishes that no-one needs to sleep, everyone ends up tired and ugly, this means that they do need to sleep, they are just unable to, this was not the wish that Timmy made.
Timmy has a birthday in four different episodes and yet always remains ten years old.
In "For Emergencies Only" Cosmo and Wanda give Timmy his own magic wand that is good for ten wishes, however the wand stops working at only nine wishes.
In "Channel Chasers", "Fairy Idol", "The Secret Origin Of Denzel Crocker" and multiple other episodes it's established that when a child loses their fairies they almost immediately forget about them. However when Timmy loses his fairies in "Abra Catastrophe" he doesn't forget about them at all.
In "Scary Godparents" Veronica's eye color abruptly changes from pink to blue during the scene when the rich kids are trick-or-treating at Timmy's house and Trixie asks Veronica to shine her costume.