I will say this, a good majority of people will respond to security/safety just by being asked. There's no need to be forceful and not only making it acceptable, but stressing that it is to others, just makes matters worse. If you tell me once and I don't listen, then fine, raise your voice a bit, but don't come at me guns blazing if I'm unknowingly doing something wrong. Plus, it's good that they're enforcing the rules, but I seriously question what rules they were enforcing with numerous things, like yelling at people during Chess to sit down because they were "interrupting the panel" (which none were...in fact, she was saying that to people that were HELPING me run the panel, no one was even close to being in the way, and I can handle my own panels).
As far as the pushing, I'm pretty sure that's assault. That should never happen, and if it's done to the wrong person you could see a shitstorm. Your security/safety team should NEVER put their hands on someone unless absolutely necessary, and there better be probable cause or proof for the need to use physical force.
Cons are supposed to be relaxing and entertaining for people. Hearing safety yell about the slightest of things doesn't help that, and the con goers are the reason you're able to run a con. They pay for badges, which pay to keep everything else afloat. Treat most people there with respect and they'll do the same. If I'm not supposed to be sitting against a certain wall, don't scream at me to move, just tell me "hey, there's an area over there to sit if you need to relax, we're trying to keep the hallways clear, can you please move over there?" I'd have happily moved. Instead I got "GET UP, YOU CAN'T SIT THERE!" screamed at me and while it got me up, it also put me in a foul mood for a bit after that.
I get these people are volunteers but the bad apples need to be removed from their position if they're causing issues. If a safety team member EVER puts their hands on a con goer and uses physical force for anything but a true safety/security reason (I'm talking good enough to call the cops for), they should be immediately removed. It's harsh, but not as harsh as using unnecessary force, and it should NEVER be acceptable.
Only other thing is, make sure that safety works with panel operators instead of just going off their own ideas. Safety got onto a few people during the Chess panel for doing things I asked participants to do (like standing off to the side to be chosen as pieces) and finally backed down after I told them I was doing it purposefully. It wasn't a safety or security issue, they weren't in anyone's way, and sure as hell weren't blocking anything to become a fire hazard, but a green shirt started yelling at them with no prior warning to go sit back down.