Other mistake: Robin says she burned the dinner because she mistook the temperature scale on the oven for Celsius. However a given temperature above -40 is always higher in Fahrenheit, so by assuming the oven to be labeled in Celsius she would have undercooked the food. For example: If the directions were to cook at 400°F, she would set it around 200°F (thinking the oven was Celsius.) If the instructions were to cook at 200°C, she would still set the oven to 200°F, undercooking the food in both cases.
Other mistake: When Ted and Robin borrow Marshall's Fiero and are sitting in the car talking as Ted drives, you can hear the beat of a song playing in the car that is not the Proclaimers' I'm Gonna Be (500 Miles), which in many future episodes is referenced as the only song that can be played in that car due to the tape being stuck in the tape player. (00:15:30 - 00:16:10)
Other mistake: At the beginning of the series, Ted starts telling the story of how he met the mother of their children. When he starts describing how he met Robin, he doesn't reveal that it was not their mother until the end of the pilot. But children should have realised it wasn't their mother when Robin said she was a journalist and worked as a TV presenter. The kids knew their mom wasn't a journalist, so they shouldn't have been surprised at the end of the episode when Ted said "this is how I met your aunt Robin".
Other mistake: Right before Barney gets hit by the bus, he's on the sidewalk. To the right there is a One Way sign pointing right, but the bus hits him driving left. The bus would have been driving the wrong way on a one way street.
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.