The “fourth” Halo 4 ordnance slot

Is there any chance you had a second controller connected? Were you continuing missions that were partially completed in coop?

I'm posting the closest information I can related to your problem. There is a known issue with completing stuff offline, but I see nothing of solo switching to coop.

From: https://forums.halowaypoint.com/yaf_postst130475_Issues-being-investigated.aspx

Completed Campaign but missing achievements Upon completing Campaign, some players find they are missing certain achievements. If you pause, you must use the "Resume Campaign" button to resume. If you choose "Rally Point Bravo" or "Rally Point Charlie", this issue arises. We are investigating but for now, replay the missions from beginning to end using only the “Save and Quit” and “Resume Campaign” options to unlock the relevant achievements.

Based on my own service record and what I remember of the few times that I played Flood, the "Other" weapon is the map itself. So falling to your death without getting shot, and I'm not sure what else would.