Yes, mobile connections are crap for gaming because of the huge difference in ping so you don't know your lead and can't predict it.
The same problem is there with low ping, the lead constantly "changes" depending on the "frame" that is processing it. (Halo works with frames, normal halo uses ~30 frames per second)
On sapp servers there are 125 frames per second(that's why your ping is lower and it feels snappier), so the change of missing the frame you predict your lead for is bigger, especially when having a low ping since there is more chance of getting in between 2 frames.
This also increases the chance of desynch issues, halo is designed to resynch when having 30 frames per second (you might notice this as a warp, when driving in vehicles)
When you have a really low ping you can miss several frames and the game can't resynch with them, so what you see on your screen doesn't synch with what happens on the server.
As a result you appear to be walking in to a wall to other players, while you might be doing something else.
Unfortunately there isn't really anything that can be done to fix this since it's both a client and server side issue.