When trying to correct something while typing, the cursor jumps all over the place and erases the wrong letters. I then have to delete the whole message and start over. Very annoying.
Sounds like some sort of ghosting. Has the screen been cracked and/or repaired at any time? Also, has there been any water damage? I ask that because sometimes cheap third-party replacement screens exhibit issues like your Moto G is experiencing. I have used an iPad that had its screen replaced by a third-party and it ghost-typed. It is very annoying! If your screen has not been cracked or repaired and the phone is not water damaged, I would recommend a factory reset. Hope that helps!
Neither thing has happened to it. Maybe the factory reset would be worth trying. Will that cause the loss of phone contacts, email addresses, etc?
If you have a Google account and use Gmail your contacts should be saved. I’d try a couple of other things prior to a reset such as restarting in safe mode to eliminate an app issue and clearing your system cache.