That's often due to dustr or grease on the tuning capacitor plates. Radios that were in the kitchen often got really greasy inside. Turned on during making breakfast, and they were virtual convection fans dragging in bacon grease. You might try a generous amount of Brake Parts Cleaner on the tuning cap.
That certainly applies to the AM band problem, but the FM issue seems to be the opposite-- maybe the FM oscillator coil needs to be squeezed a bit tighter?? Dunno. These things are often mysteries. Longago I had a BC-221 frequency meter, WW2 vintage. The main coil had somehow, inexplicably, lost some inductance. This is a silver-plated wire tightly wound on a toothed ceramic form, so thr coil moving sounds unlikely. I ended up having to place a very small ferrite tuning slug in the middle of the coil to get the frequency readings to match the codebook. BTW does anyone know that Philco made a digital frequency counter in 1940 just to automatically print these codebooks, one for each BC-221?? ? Amazing.