This is the second time I run into this:
Switching input language by taping (and holding down) the the space bar and sliding it left/right does not work on Samsung Galaxy Note 2.
So I decided to write a “Note to self” post, because fixing it is not at all intuitive.

Everything in the keyboard settings is set right, the problem is not there.
The problem is with some weird interaction with accessibility services.

The sliding language selector does not work if any accessibility service is turned on.

After switching it/them off it works like a charm. Switching any of them on breaks the keyboard…

There’s definitely some bugs here, cause when a service is turned on and the Accessibility panel shows it as on, after I tap it and the service page is showed the on/off slider is in off stage. I have to turn it on and then off to actually be able to turn it off.

It sure would be great if someone fixed that.