My bluetooth keyboard and mouse are choppy Problem

My mouse is choppy as I drag it around the screen. The buttons on my keyboard occasionally get stuck "on", resulting in a bunch of spaces, or periods, or triggering the special character pop-up for other letters, or deleting too many characters.

System

I'm on OS X 10.9.5 on a late-2011 Macbook Pro.

I use a wireless Apple Mighty Mouse and an apple wireless keyboard. Both communicate over Bluetooth.

Battery is reported at 59% for the keyboard and 46% for the mouse. I've previously been able to run these down to 20% and lower without any negative effects.

The devices are approximately 40cm from the Macbook.

What I've tried

I've turned bluetooth on my Macbook on and off. I've disconnected and reconnected from each device. I've turned each device off and on. I've rebooted. Bluetooth on my nearby phone is turned off.
I'm not sure if this is the problem you're having but I was struggling with this for a few months until I realised my mouse was sometimes too far away from the laptop. The laptop was on the left side of the monitor and the mouse on the right. I switched the laptop to the right side and it's working flawlessly :)