Continuity mistake: During Christian and Ana's last Red Room scene together, there's a moment when Christian rubs, I'm assuming, some oil on Ana's body-more specifically her chest and breasts. When Christian enters her while she's on her side, there's no indication that the oil is still on her body, and Christian rubbed a lot on her. This is a continuous shot, so I doubt it could have dried up that quickly; it's also more noticeable when she's on her back and you can see the area(s) better.
Continuity mistake: When Christian and Ana are making out just before having sex for the first time, Ana's hand is on the back of Christian's neck when the camera is facing her. Then when the camera is behind Christian, her hand isn't there, and it goes back and forth until from behind Christian we see her hand slide around his neck.
Continuity mistake: When Jack is at the masquerade ball, he takes a photo of a picture of Christian and his family. If you look at his camera, you'll see that the frame is barely being taken. However, when Jack looks at it at the end of the movie, almost the entire frame can be shown in the picture. He had no reason to take another photo, and he left right after taking it.