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 "Foul Balled", Timmy wishes that Chester was the best baseball player ever and he starts winning every baseball game he plays in. However, it's said in many episodes that magic can't be used to win competitions.
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 "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 "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 "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.