Bluetooth keyboard causing wifi to freak out, in turn using all of my CPU and RAM?
Bluetooth and WiFi do use the same 2.4GHz1 frequency bands (as do many other things), so they could interfere relatively easily. It also doesn't help that there are a lot of networks in your area. However, I find it highly unlikely that the interference would cause you to lose your connection, given that the video shows a full 4 bars when you are connected.

Personally, I would suspect a hardware issue in this case. The Bluetooth and WiFi connections are most likely controlled by the same chip in your computer, so it may be malfunctioning only if both of its services are being used. Try reproducing the issue on someone else's wireless network, and take it in to an Apple Store if you can. If you cannot reproduce it on someone else's network, it may be that your router is picky with its connections, or something else completely.

1 802.11n does allow using a 5GHz band instead, so you could try that if your router and computer support it. It isn't very commonly used yet, so there is typically little interference there.