Gnome Software keyboard weirdness
I also had this problem, did some searching and found this. It fixes the issue for me no longer getting double letters
Install ibus-gtk In the terminal do
sudo apt-get install ibus-gtk ibus-gtk3
Reboot. (Does not work until rebooted)
Should work now!
I had the same problem after upgrading to 16.04.
I had previously disabled IBus when I was running <=15.10 due to an issue with the Jetbrains Pycharm IDE.
Renabling IBus fixed the issue with Gnome Software for me.
Try opening your system Settings > Language Support and ensuring the Keyboard input method at the bottom of the page is set to ibus. If it was set to none, reboot after you change the setting.