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.
The Wedding - S1-E12
Plot hole: After Claudia's call, they decided that Lilly will meet her at the bar and the guys will meet Stuart. They're all at the apartment at the same time and the dudes have gotten to Stuart's apartment, convinced him to still marry Claudia and then go back to the bar right after Lilly gets there. And also giving a lot of time to Barney hitting on Claudia. There's no way that could happen in this order, they live right above the bar, Lilly was supposed to be there before Claudia.