Other mistake: The scenery in the "I Love Lucy" on-stage scenes shows the Ricardos' apartment with a living room window. That was the apartment they moved into after Little Ricky was born. Before that, they lived in an apartment with no (visible) window in the living room.
Other mistake: After seeing Joe Montana play in Super Bowl XIX, young Kurt said, "I knew I wanted to be that guy." When he goes outside to pass the football, young Kurt has "Warner 13" on the back of his jersey - not Montana's #16 but the #13 that he could not know in advance that he would eventually wear during most of his adult career. (Jersey numbers are not necessarily that available for a player to have his pick). (00:02:02 - 00:02:33)
Suggested correction: This is trivia at best, certainly not a mistake. While it's true he wore #12 in high school, there's no reason he couldn't have liked #13 as a child. And, many key position players do get to pick their number, from the available range, which Kurt certainly did.
Other mistake: It isn't clear if the poster of the Solar System outside the school was cut off on the right, showing half of Neptune, or if the ninth planet at the time (Pluto) was accidentally omitted. IF the poster was supposed to be complete, its exclusion of Pluto would be an error for the time period (1969) because Pluto was not downgraded to a "dwarf planet" until 2006. Perhaps, only half of Neptune was shown in order to not have to address the changed status of Pluto, making this a deliberate mistake. (00:32:36)
Suggested correction: Neptune isn't cut off, it shows as a complete circle on the "poster" (looks more like a board).