Plot hole: Caroline helps Max get her degree, since Max didn't graduate high school. However, in episode 5 of season 1, Caroline and Max are raising money to pay off Max's student loans.
The Mothers - S3-E17
Plot hole: When the "refrigerator" falls on Tobias's mom, the boys are watching from a side view. It is later revealed that the fridge was just a cardboard cutout. The boys were watching from the side, so how did they not notice it?
Episode #1.5 - S1-E5
Plot hole: Leon Hamilton is the most hated man in Sainte Marie, with over 900 people on the island conned by him. Yet exactly one person in the whole island knows how he looks like, every newspaper and website never ever published a picture of him even during the very public trial when they were trying to get their thousands of dollars back nor publish an archive picture after his death.
Casus Belli - S6-E5
Plot hole: Later in the evening, after NYPD takes Quinn into custody, Carrie finds his cell phone, with pictures showing their home had been spied upon from across the street, as well as other evidence of a conspiracy. He had tried to hand her the phone right after the police broke in, but it was knocked from his hand and she discovered it under the smashed door. In the real world, Carrie's home would have been considered a crime scene and the police would have searched it thoroughly, top to bottom, undoubtedly finding the phone themselves, but are shown driving away after the confrontation.
Plot hole: It's been established that if you die on the property, you remain as a ghost for all of eternity. However, in Season 8, Moira's bones are retrieved and buried in a cemetery so that her ghost can escape and join her mother. However not all the ghost's bones are buried on the property, we know for sure that the Black Dahlia was not buried on the property and it's not likely Tate, Vivian, Ben or some of the others are buried on the property as well so they should not be tied to the house.
Suggested correction: Tate's victims from the school shooting are ghosts who can move between different locations. There's nothing to suggest that the ghost of the Black Dahlia isn't merely choosing to be in the Murder House rather than being tied to it. The same goes for Vivien and Ben, since Violet is going to stay in the house, so might they.
New York City Serenade - S3-E12
Plot hole: When talking to Hook about the photos, Emma states he could have photoshopped them to make it look like she and Henry were in Storybrooke, however she had taken them directly from Henry's camera and had them developed. So Hook had no way to photoshop the pictures from inside the camera. (00:27:00)
Plot hole: Skye's mother, Deborah, was held hostage by the Sixers for several years, though everyone believed she had died in an epidemic and was buried in Memorial Field. The Sixers kept her alive with medicine only they had to force Skye to act as their spy. Even though Terra Nova has a medical clinic staffed by doctors and nurses, it was never noticed that no one had witnessed Deborah dying, her body was never placed in the morgue, that was there no record of her being buried, or even questioned that there was no corpse. Deborah just disappeared without a trace and nobody wondered about it.
Plot hole: This was the first episode of the series and we see that the rangers are unable to figure out how to properly operate their zords; but in Origins Part 1 (which takes place prior to this) they have no issues with the zords at all.