If you want your videos to appear on in your Theater and YouTube do this first :-

Go to YouTube.com and create an account using the same email address as you have registered with on this forum.
Then click the Theater button at the top of this page.
Login using the same Log in details you use for this forum.
While on the Theatre page there is a link to YouTube link at the bottom of the page.
You should then be taken to a Google/YouTube page with an Allow Access Button, click this to allow callofduty.com to upload to your YouTube account.

Once done load up your COD BO on your Console.
Goto Xbox Live Then Theater
My Recent Games (this will have videos of all your recent games)
Select the Game from the list you suspect or know contains a bug,
Then press Select for playback it will then download the game to your console.
Then press Start Film and watch through to where the Bug/Glitch/Spawn event happened (note you can fast forward with RT (note the RT works like an accelerator the more you press the faster if fast forwards) once you find the part you want you can press LT to step back 10 seconds.
Pressing A will pause the playback so you can start recording from that point by pressing X, Pressing X a second time will end the recording. (Note: you can only upload 30 seconds of video)
If the angle is of the recording does not show what you want others to see, you can press Y and go into FREE CAMERA MODE which will allow you to move anywhere by using the Analogue sticks so you can get a better angle (if your recording Spawn issues you could Fly high up into the sky and look down on the action or swing the camera round so you can the opponent Spawning behind you)
After you end recording you can Preview the Segment or Discard it.
If your happy with the recording You can Name and Categorise it The you can Upload the clip, Press and choose a slot from the Six available in your Theater, Press A to upload the Clip it should then upload and be visible in your Theater on your console (note not on the web yet)

To upload to the Theater on callofduty.com and YouTube
Go back to Theater on the Console,
Then my file share,
Select the clip you want to upload by pressing A
You can preview the clip by selecting Start Clip
If your happy with the result Select Render Clip
Then it should Render and Upload to your Theater and YouTube automatically (this takes a few minutes to complete) if it is successful you video will show up within a few hours both on your Theater on callofduty.com and YouTube, it will not show on these immediately)

If you get a error appearing on your Theater saying invalid token I found that by powering down my console and re-rendering it it worked

Hope this helps.

Here's my first one of a Bug with a CarePackage I called in http://www.youtube.com/watch?v=FhumkRai4f8