I think you should go to management with the concerns you have with this intensivist. It is NEVER acceptable to hang up on another caregiver on the phone. It is NEVER acceptable to not listen to nursing concerns about patient that he is covering. This is an attitude that needs to be broken, and quickly.
The issue with the respiratory order (CPAP/BiPAP?) - IMO, it is absolutely the RT's responsibility to be checking their orders and doing their own work independently. They have a license too. If you have an RT that covers your unit and isn't floated 15 other places, this should be an expectation. This is one of my pet peeves, actually -- I have worked places where RT is great and they do everything, and I have worked places where you have to call them for every little thing. (I'm also a little confused in that it was a new order but the patient was on it the night before -- what's up with that?) Is it your responsibility to notify RT for these kinds of orders? Is it something the clerk could have done, but missed? Did RT not see the patient for the entire shift anyway? Were they supposed to be following the patient? I would talk to management as well about the RT role and what the expectations are. Yeah, maybe you dropped the ball (maybe....not 100% sure on that, especially since the patient was fine) but RT should have picked it up and ran with it.
Being overworked and exhausted does no one any good. Man, I feel for you. I have seen this kind of crap go on and on 100+ times at a number of facilities. I wouldn't pin this on you, actually -- your system is a crappy system -- obviously it failed here. I hate it that this kind of stuff gets pinned on nursing all the time -- and actually, you pinned it on yourself!
Let me give you a piece of my very best advice. Ready? Here it is: DO NOT TAKE FULL RESPONSIBILITY FOR SYSTEM ERRORS. Learn to recognize yourself as simply being a piece of the problem, and don't personalize it. This was you in this instance, but it easily could have been one of your coworkers. This involved other departments and other caregivers. If you keep on pinning this all on yourself, you are opening yourself up for disciplinary action for issues that aren't entirely yours. Don't do that.
Did you do an incident report on this? I feel that it warrants that, since an ordered treatment went 8-12 hours without getting implemented -- if we missed 8-12 hours of an antibiotic, we'd have to write it up. I see this as being a similar scenario. Hopefully you did, and somebody that can actually do something about it will examine the situation and try to fix how things operate around there (I wouldn't hold my breath, though, unless you have some managers that are really good at/like operations.)
Anyway, that's my two cents.