I would put some screws in the bracket into the stud to reinforce it. The box itself is fine. The cable clamps look a little suspect to me, though. I can't really tell from the pic, but it appears to me those clamps are for metal flex cable, not non-metallic cable.
Also, in the lower left hand corner, there's a hole with threads tapped into it. This is for connecting the bare ground wire to the box. Please use it. A 10-32 machine screw is all you need to secure the wire.