I paid attention and made some conclusions, then tested and found to be true. Here goes:
Killstreak stuck - showing PDA pressing a button several times, then hand is hidden and no weapon is selected, killstreak is not used, I have to press Killstreak button again to go back to my weapon, then pressing the button again (not two killstreak buttons, but only one) makes it work properly
Bulletproof Vest stuck - bulletproof vest is lying on the ground, but can't be picked up, doesn't give XP, doesn't count towards used killstreaks, and can't be dropped again (unless I use a different killstreak, then it works).
Care Package marker stuck - care package marker was dropped, but doesn't create red cloud and doesn't call in care package. Can't be used again till respawn, because it says "no ammo" when selected.
Now I'll explain how to make this happen (tested all but care package).
To get a stuck killstreak, like SatCom:
Press killstreak button together with another killstreak button. Even if you can't use another killstreak, it'll get stuck.
To make bulletproof vest stuck:
Simply drop it on the ground and quickly press Use button (F in my case) before it lands. There - you can't use it, even though its right in front of you, on the ground.
To make care package marker get stuck:
Throw a care package marker and quickly call in another killstreak reward, before the marker is activated. There you have it - care package marker script is cancelled, care package marker is thrown out as if it was a tactical item, and you can't throw any more of them.
To make care package unreachable (bonus):
Simply drop the marker into unreachable spot or drop it in a building! There you have it, a bug that was fixed back in Modern Warfare 2 by making the crate jump around till it lands into reachable area (or it did get cancelled if dropped outside of the map?).