No. Never at anytime blame anyone else but yourself - even if you were not at fault. I am not trying to be condescending, I am just saying what the interviewer wants to hear.
Take responsibility for it - admit it was your mistake and more importantly what you learned from it. A warning letter is just that, a warning. No action was taken. The interviewer will want to know what you learned. THEN you can bring in how you felt that the organization did not provide you the best information (do NOT bad mouth them!!) and you feel that a mistake that grave, not telling a pilot an airplane is grounded, is reason to separate yourself from the company.
For your floating job, did the name of the company atop your paycheck (or direct deposit slip) change at all? If not, they I would just list it as one company.
If you list your permanent address is NJ, why not use that? I too have been bouncing around places (all in same area) while at college and now my new job. I think list something that you feel you have and will be at for the longest.