Changing the state of Packet Coalescing seems to solve the problem temporarily (turn it on if it's off, or turn it off if it's on). I have 3 BT devices connected to my Surface Pro and the mouse would lag horribly whenever anything was playing through the earphones. It stopped lagging once I changed the Packet Coalescing option's state. However, it came back after I did something to trigger it, which I have yet to determine. Ugh.
I have a Surface Pro 3 (i7, 512GB). After working fine for several hours using a Bluetooth keyboard (FILCO) and mouse (Microsoft Arc Touch), I started experience the lag issues described on this thread, both with the mouse and the keyboard (keys would occasionally stutter, as if the key-up signal wasn't received). Turning Packing Coalescing off, as suggested above, has done the trick so far. Hopefully it's stays fixed!