When Isak is standing under the clock in his dream his face is in shadow but when he walks away a few moments later there is no shadow on the face or the wall.
The front license plate on the VW disappears when untying the rope.
When they are in the car and the professor told Marianne about his dreams, about him living although he is already dead. Marianne then tells him what she was thinking, earlier, when they met his mother. She had referred to his thoughts being a living dead although he just told his dreams, she did not know anything about his dreams before they met his mother.
It has been included as a continuity error that Marianne says she is going to go swimming at the old house, but when she returns her hair does not appear to be wet. This is not a continuity error, because when the film was shot in the late 1950s, and for at least a decade afterwards, at least in the Nordic countries women gathered their hair up and covered it with a special swimming cap to protect their hair from becoming wet. Some women who had grown up during those times used swimming caps as late as the 1980s, because they had grown up with the custom, and a swimming cap was to them just as integral part of swimming attire as a swimming suit.
On their way in the car after Isac visited his mother, he dozed off. Car is in move and for a split second, background falls in black from scenery, showing that it is rear projection.
When Isac is walking with the others to the ceremony house, you can see 2, presumably, set photographers on one of the the front yard columns at the back.