A star's magnetic field does have some mechanical effects on anything nearby that is either ionized (like interstellar gas) or conducts electricity (like the plasma in a nearby star). Mechanical magnetic effects on the rotation speed of a star are minute, but measurable.
For example, the rotating magnetic field of a spinning neutron star can thrash electrons in the interstellar medium so hard they are accelerated to relativistic speeds and give off visible synchrotron radiation (like the Crab Nebula). This transfer of mechanical energy causes the spinning star to slow down.
If a star is rotating within another star's magnetic field, it will encounter some resistance due to magnetic braking, though gravitational tidal forces are probably vastly more significant. On a smaller scale, convection currents in the Sun are impeded when they are forced to move across magnetic field lines; and this is why sunspots are cooler than the surrounding regions. (The rotating disk in a typical power meter, which passes through a pair of damping magnets, is another illustration of this principle.)
Well put.
Planetary rotation will also cause arcing and sparking in whatever atmosphere is present. Rotate metal through a magnetic field and you get electricity, after all.