During the flashbacks to 1000 years ago, Klaus says "We were just having fun." But the word "Fun" wasn't invented until Shakespeare times, about 500 years after these flashbacks take place.
When Damon is laying in Elena's bed, after she says that Rebekah allows love to "consume her, Elena rolls to her side to face Damon. Damon rolls onto his side to face her. Elena says, "I'm not mad at you for letting him out, Damon." She then reaches to turn off the light on the nightstand. When the camera angle changes and they cut to a wider shot, Damon is on his back again. When they cut back to the close up is on his side again.
The Story told by Rebekah about Klaus' father (and how the war between the vampire and werewolf species began) contradicts the story told about Klaus' father in the episode Klaus.
Elijah said that Mikael killed Klaus' father after finding out that Klaus wasn't his son while not realizing that Klaus' father was a werewolf and he was starting a new war between species.
Rebekah said that Mikael learned that Klaus wasn't his son after Klaus triggered his werewolf gene. This means that Mikael was aware that Klaus' father was a werewolf.
However, it is possible that Elijah's statement referred to the fact that Mikael was unaware that werewolves from all over the world would retaliate against his attack.
Klaus cannot get into the Gilbert house as he has not been invited in. However, both Elena and Jeremy have died at least once meaning the seal should be broken and all Vampires should be able to enter.
In the Reckoning. When Stefan is running after Elena, he runs into the cafeteria to stab himself but when he turns around you can see the point of the stake and that it did not enter him.
When Caroline was captured and tortured by Alaric, she had two pencils through her hands; however, when Elena got the chance to escape with her, she only pulled one of the pencils out.