Has the keyboard app you use had an update recently?
May be worth a uninstalling and then reinstalling the keyboard app.

 

swiftkey is a very good replacement keyboard and it's free

 

Plus one for Swiftkey. Way better than any stock keyboard app.

 

I had the same issue on facebook in Chrome. It might be chrome somehow since I have no issues anywhere else.

 

I was also having this exact same issue last week. Back space would create some random words, or create a double of the word I was trying to type or it would even move my cursor to an area that I wasn't even typing in. Very strange and odd behavior needless to say.
I was also having and issue with OK Google command not responding correctly.
Updated them both and haven't had a problem since.

Chrome was just updated on 10/09, so you might want to try and update chrome and see if that remedies the problem for you - https://play.google.com/store/apps/details?id=com.android.chrome

 

Those of you with this problem - are you using the stock keyboard app? If not I suggest to changing to another app to see if that solves it. I use Swiftkey, and I have not had this problem at all.