The window frame on the driver's door doesn't fit tight to the body seal at the upper rear corner. The fit is good at the front portion of the window and at the rear bottom of the window where the window frame meets the door. With the door closed, sitting in the driver's seat, you can see the gap increases at the top of the window frame from front (window frame is tight to the seal) to rear (window frame does not contact the seal). Otherwise the door's gaps are good and the door is flush the adjacent panels.

Can the window frame's position be adjusted?

Yup very easy fix, put a lump of wood in the door opening to stop the door shutting and just pull against the top of the window frame (with the glass down) to bend it back into shape.

I've been thinking that this might be the course of action I need to take.

Is it just the window frame or the whole door? If you check the door hinges there are usual spacers used adjust the position.

It appears to be just to window frame. The alignment of the door itself to the rear door and the fender are good. But I suppose a small adjustment at the door hinge would make a big difference at the top of the window frame.