No North American house built in the 1600s would have a basement, even less one as tall as shown in this film. It would more likely have a root cellar and not one that extended the full footprint of the house.
When George is chopping wood and Billy is holding the second log, George swings the axe back, and when he's swinging the axe at the log, that Billy is holding, he doesn't have the axe on his hands. The axe reappears when he chops the log.
When Kathy sits down in the library to read Chronicle of a Zealot she flips through the pages and you can clearly see that the pages are completely empty and appears to be from some kind of notebook. She then finds what she's looking and starts to read, the camera cuts to another angle and suddenly the pages are filled with old fashioned printing.
While the realtor is showing the Lutzes one of the bedrooms, she looks back to see a shadow in the hallway. When she looks over she's in the living room, then when she turns back around she's back in the bedroom with the Lutzes.
At one point the Lutzes are in the kitchen and the refrigerator magnets read "Home Sweet Home". In a rage George knocks the letters down. In the next shot, the letters spelling out "Home" are visible in their original position.
In the bedroom when we first see Jodie in the rocking chair, Chelsea places her index finger over her lips, indicating she is whispering to her new friend Jodie. In the next shot, she puts her finger back down to her lap, but then we see her finger back on her lips and places them down a second time.
When Kathy and the kids are getting down from the roof after being chased by George, we can see Billy, Chelsea and Kathy get to the stairs in that order, leaving only Michael still on the roof. In the next shot Kathy ask Chelsea to jump because she's on the roof again with Michael.
The actual address of the house when the Lutz family moved in was 112 Ocean Avenue. When George and Kathleen visit the house for the first time, the address is 412 Ocean Avenue. This is because not only is the movie not meant to be historically accurate in any way, but for legal reasons they were unable to use the house's original address. For the same reasons, the children's names have been changed from the original Lutz family names.
When the door in the basement opens, George appears with a pump action shotgun. He cocks the shotgun, loading the chamber with a live round. As he chases Kathy and the children through the house, he cocks the action again, which would eject the previously loaded shell, and no shell was ejected.