I have a wall switch that is not working right.

The switch should work like this: push the button and light turns on. Push it
again and light turns off. It's a three way switch imho. It is also the only
switch to the light in question that I know of.

Now the switch works a bit strange. When I press it the light turns on. When I
press it again the light does NOT turn off. Multiple press and nothing happens. I
let the switch be for about ten minutes and the tried to turn off. The light
turned off like it should. This is how it works now: it will turn off only after
some time passes.

I switched power from mains and examined the switch. I appears OK and looks just
like a simple switch. I pulled out another three way switch is is identical and
works OK. The wires were connected identically although.

Leaving the switch off with neutral and hot wires dangling in the air I turned
mains on. Suprisingly the lights were on!

What could be the problem? The switch is probably broken but how come the light
could be on when the hot and neutral were cut off??