How to fill between door frame and tile
The usual approach is to cut a thin strip of the same jamb and moldings and glue into place.

You can also fill in small spots with an epoxy based product like Bondo or other paste-like filler (would not use it for thicker vertical surfaces since it may slump). It can be carved and sanded like a hard wood.

A combination of these techniques should give you a pretty unnoticeable surface once painted.