If the place is as bad as you've suggested, chances are good that staying jeopardized your licensed. I would definitely put things in writing, but be careful and professional in what you write to them. Something short and sweet such as you did not agree to mandatory overtime when hired, inadequate staffing, poor patient care, etc. Less than a page. Since you did not pass your probationary period, I wouldn't be too concerned about not giving notice. Staffing is their problem, not yours. It would have been nice to let them know you weren't coming back, but it really takes an idiot not to be able to figure that out when you show up for work then don't stay and work your shift.
You might also consider, though, that the calls may be because they would really like to keep you, already know their place is a disaster, and you aren't the first (or last) to leave. Yet, like most Machiavellian employers, they think a few threats "sweeten the pot" instead of trying to treat you better. If they are threatening you with calling the SBON, I figure you don't owe them a thing. If you choose to do anything at all, it would be a courtesy, not a necessity. I differ somewhat with the above comments since I've been on both sides of the fence. I hate it when people quit suddenly without giving me a chance to straighten things out first. On the other hand, a good facility wouldn't have the problems you suggest in the first place, so shouldn't be too surprised when they can't keep staff.