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.
On season 5, episode 21, Barney tells a story of how he had sex with a portuguese contortionist. Later that season, in episode 24, on his map where he marks every country which he has had sex with someone from, Portugal is unmarked.
Because during most of filming of season 3, Marshall had longer hair there are several flashback moments of Marshall in the time line of the first two seasons where he has long hair, but when the first 2 seasons actually took place he had shorter hair.
Marshall, Lily, and Ted went to Wesleyan, where Ted studied to be an architect, but Wesleyan does not have an architecture program.
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.
In the Halloween episode in season 1, Robin says she never played any team sports. Just Tenis. However in a later season she mentions how her dad caught her kissing a hockey team mate.