Factual error: The way Barney employs the green screen wouldn't work because a camera is needed to put a picture over the screen. To the naked eye the screen would still be green. The only plausible way to make the illusion work as intended would be a regular white screen and a projector, but this isn't the case here.
Continuity mistake: We find out in this episode that Ted and the mother don't get married for several years, due to postponing the wedding when she became pregnant. They eventually get married in 2020, when their children are 3 and 5. But in Lobster Crawl (8-9), at the end of the episode Lily and Marshal show up to babysit Ted's daughter when she's younger than that, and Ted is wearing a wedding ring.
Continuity mistake: Marshall tells Lily that he has never been to the ladies' room of the bar. However in the second season episode "Showdown", Robin catches Lily and Marshall "holding hands" in there. And in "Of Course" in season 5 Marshall, Ted, and Lily go in the ladies' room to comfort Robin.
Other mistake: There is absolutely no reason for Ted to hang around underneath his apartment window while Jeanette is throwing stuff out of it. Any sane person would know that there is a very high chance of getting struck by the myriad of Ted's belongings that are wantonly chucked out onto the street. He's not trying to collect/catch anything because he is turned away from the building, and is not paying attention to the items that are being thrown out.