huh? not sure what you mean by broken, but if you mean what I think you mean then none of the weapons/plasmids are really broken... if I had to pick one I guess hypnotize (or w.e the one where you get splicers on your side) because sometimes they'll still attack you or will just stand there.
Besides that I didn't find anything about this game "broken". Although I haven't played the multiplayer.
Electrobolt + Speargun is still a ridiculous one two punch, though you don't have to rely on it quite as much in this game with how much more balanced the weapons are compared to Bioshock 1.
I can't think of anything really game breaking off the top of my head, though Security Command + Handyman can be situationally overpowered. I killed a couple Big Sisters without getting hit by just hiding behind my bots, repairing them and giving supporting fire as needed. Channeling level 3 plasmids with the machine gun (or anything really) can be pretty potent, but incredibly resource draining. --- Go Stanford Class of 2009!
It's not conventional, but the Rivet Gun was my go-to throughout the game. Plentiful ammo, and it basically one-shots all splicers (save brutes, of course), provided you get headshots. --- "We are the greater good." -- Rick Grimes, The Walking Dead
I was surprised to see that I had the same conclusion as others - mostly b/c I'm not a great gamer and so I tend to find things that are broken to a skilled player to be reasonable to me.
What I'm referrring to is that no one thing is broken. One thing I adored about both B1 and especially B2 is how fun it is to use literally every weapon.
With that said, I think there are a couple ways I often employ to just steamroll my way through the game, even on its hardest difficulty: if I'm looking to save myself from taking damage, I'll use Insect Swarm and pick the baddies off from afar with the spear gun or, if I'm looking to just be a glass canon, I'll usually try and plan - I felt there were explosive tanks all over the place in B2 and I'll telekenesis + rocket launcher + inferno to keep the party goin.