Any ideas ?

I have a new-ish 2+ year old iMac, (the first of the new slim models). With that I have the standard issue wireless keyboard and 'magic' mouse.....

Every once in a while something, I'm guessing the keyboard, throws a wobbler. Typing anything anywhere just finds additional letters being added in 1's and 2;s. In the case of yesterdays bout, I,T, and U.

Switched off and on, checked obvious things, to no avail. As before, leaving it switched off all night seems to resolve it, and I'm guessing it'll be OK for a few months now.

Any ideas, duff keyboard maybe ?

Batteries?

Had the same sort of trouble with a mac pro:
https://discussions.apple.com/thread/5226740?start=0...
It's unfortunately quite common, I ended up replacing mine with a usb keyboard.

I would check the batteries, using the more expensive type helped for a while, also check there is no other equipment nearby that may interfere with the signal.

Replaced, but thanks for the suggestion.

Thank you, will have a read through that later.

I had a similar issue with a mighty mouse frequently "forgetting" that it was paired to my iMac.
In the end, after doing all the usual NVRAM & PRAM resets, what cured the issue for me was to go to the bluetooth cntrol panel, then select the offending item, delete it and let it re-pair it with the iMac and it's behaved itself perfectly since then.

You may want to check if there's an actual bluetooth preference file, in case it has become corrupted. If you trash this, then log out and log back in, then you should find that the system's created a new preference file in it's place.