Spotlight and Alfred can't find Photo Booth
Your Spotlight index might be corrupted – Alfred uses the same index as Spotlight.

If Photo Booth is the only item missing, you can try dragging it out of /Applications (to your desktop, say), then back in. You’ll have to authenticate as an administrator both times; Spotlight should pick up on it after that, and so should Alfred (after a small delay). If that doesn’t help, or other items are not found either, you will have to re-build the Spotlight index, either by following Apple’s official procedure, or via the Terminal command sudo mdutil -E /.