I have been having this same issue since day one with my Surface Pro as well. I have been troubleshooting this every way I can possible think of, and here is what I found:
- The bluetooth lag affects both bluetooth mice and keyboards (mouse lags, keyboard lags and repeats keys at random)
- It happens when outbound data is completely saturating the WiFi connection on 2.4 Ghz AND 5 Ghz.
- Saturating inbound network connections has no effect.
- This occurs with all current Microsoft bluetooth keyboards and mice. I have tested them all.
- It also occurs with Logitech bluetooth keyboards and their ultrathin touch mouse (awesome mouse, by the way....much better than the Microsoft Surface touch mouse).
There appears to be an inbound bandwidth issue with the Marvell chip that is causing bluetooth connections to become such a low priority that it causes delays and data glitches in the case of repeating keys on bluetooth keyboards.
Hopefully the Surface Pro 2 uses a different chip....