The Man in the Fallout Shelter - S1-E9
Plot hole: At first the victim (Careful Lionel) is described as not returning to pick up his new shirt in November 1958, and possessing love letters dated from 1957 through early winter (November) 1958. Booth reports the fallout shelter where Lionel's body was discovered was sealed in 1958. Later Lionel is described as reported missing by his boss in January 1960, and the illegitimate child he fathered was born in 1960 as well. That would mean his boss didn't notice he was gone for over a year, and his pregnant girlfriend was with child for at least 14 months.
Plot hole: The ages of the children on the show are really inconsistent. When the show starts in 50 BC, Octavian is around 12, Lucius is an infant and Vorena the Younger is at least 8 (given that she must have been concieved before Vorenus left for Gaul). Three years later Caesarion was born. When Simon Woods takes over the role of Octavian, Octavian is around 19, as stated on the show. Lucius should be seven but looks like he's four and Vorena should be fifteen but still looks eight. Episode 9 of season two takes place in 32 BC, 18 years after the first episode. Octavian might very well be 30, but Lucius (who would be 18) is around seven, Vorena (who would be 26) is a pre-teen and Caesarion (who would be 15) is around eight. Even if the events were moved up so that episode 9 is actually set earlier, the ages of the children still don't match when compared to how much the other characters have aged.
Plot hole: When Robin and Lily find Barney's secret Robin notebook, Barney and Ted are at the class, so Barney should have the notebook with him.
Suggested correction: This is a character mistake at best, and quite a common one. Students constantly forget their textbooks, homework, notes, supplies etc.
It should be noted that the plot hole isn't talking about "students." This isn't about forgetting textbooks, supplies, or homework. Barney is trying to be a better boyfriend to Robin and wants to learn Ted's secrets since Ted had dated Robin. If Barney has been writing everything down before, the mistake is pointing out why isn't he writing it down this time, except to allow the writers to have Lily and Robin find the notebook and the class.