On the level “Reclaimer”, weapons have a tendency to actively vanish. I killed a Grunt and had one Rocket left in my Launcher. I figured I would take out the Ghost guarding a watch tower with the Plasma Pistol and a Plasma Grenade. So I picked up the Plasma Pistol, and as soon as my Rocket Launcher hit the ground, it and every other spare weapon around vanished.
That happens in every level.
Yep.
I’m glad I looked into this before I got Halo 4.
But at least weapons don’t fall through the ground like in Halo 3. 
It’s a shame there are very few levels with marines, as a good workaround would be to give the weapons to the marines to hold onto, as noted here.
If you haven’t installed disk one onto your hard drive, I’m going to recommend it, bugs and lag issues appear less frequently sometimes even not happen when it is installed, I played missions 1 and 2 without installing it on the hard drive and it worked fine still, but try installing the game then giving it a go