Twice recently on TV I've seen the sun appear to move from right to left on the screen....?

the simplest reason would be that they are looking from the south rather than the north. That switches right and left with respect to east and west. West moves from your right side to your left side, and east from the left to the right.

Left and right are not universal directions. Move to your left. turn around and face the other way, and move to your left. If you followed directions, you are right back where you started.

You may be seeing the effects of how the shots of a film are commonly made out of sequence on different days and at many different angles. The director may shoot a scene that appears later in a film, before he or she shoots a scene earlier in the film. The director will try to keep the relative time of day consistent from one shot to the next when the time frame of both are supposed to be the same, even if they are shot on different days, but may not pay that much attention to the logical position and transition of the sun, feeling that perhaps no one will notice. I have seen similar inconsistencies, such as changes in length and angle of shadows between two consecutive shots and this is the reason; a director not paying enough attention.

If the camera is facing north, then east is on the right and west is on the left. If the camera is facing south, then east is on the left and west is on the right.