How I Met Your MotherGoofs
When Lily is approached by the girl that's been sabotaging Barney while he's trying to pick up girls, the girl's hair is wavy/curly - and her voice definitely not Britney Spears. Later we find out that the girl who talked to Lily was Abby, Britney's character, and the scene is shown again - this time with the actual Britney in it, straight hair and all.
Incorrectly regarded as goofs
In Single Stamina (2.10), Lily and Marshall are married at Barney's brother's wedding, as evidenced by the rings on her finger, and Marshall's reference to her as his wife. At the scene, Ted and Robin dance, which indicates that they might be still together, even though during Something Blue (2.22), in which Marshall and Lily get married, Ted and Robin are broken up. However, the fact that Ted and Robin are not tired at the wedding (having Single Stamina) while Marshall and Lily are tired (having Couple's Coma) indicates that they are broken up, just on good enough terms to dance with each other.
The time on the clock in the apartment is always 4:20, at least during season 1. This is deliberate joke, since 4:20 is a code for smoking marijuana, and both Ted and Marshall use marijuana multiple times throughout the series. In any case, a wall clock can be broken or decorative even in real life, so it's not a mistake either way.