This sounds like one of those problems that's caused by more than one fault. If the contacts on the thermostat are badly burned, the arcing can cause nasty spikes on the mains. This can also lead to RF interferance.
Do the lights affected, by any chance, have dimmer switches fitted? If so, it could be RF interferance with these, causing the problem.
If the capacitor is stuffed (not a very common fault), this could lead to fluctuation of the mains voltage during the transitions from on/off off/on. These would not normally, however, have any significant affect on your lighting circuit, unless your cabling is substandard in the first place.
If the bearings on the motor are knackered, this will place a heavy load on the circuit as the motor fires up. When stopping, however, there would be less back EMF than a normally operating motor. So this fault should not manifest any external symtoms, on the transition from on to off.
Worn thermostat is my best guess. They're pretty cheap to replace anyhow.