I am very sorry this happened to you, and I can only imagine your embarrassment when that door opened; certainly this event should never have occurred and undoubtedly it could have been prevented. Having said that, and knowing that I am not a lawyer, I do not think you are entitled to any legal remedy.
Anyone who is a guest on another person's property has a right to some level of Standard of Care. That level is different in a person's home than in a business, and every business is different, as well. What is true, though, is that the Standard of Care must be uniform for every establishment in a particular category (i.e., hotels).
Standards of Care protect guests against accidents that occur on a property that are not caused by a third party such as a person falling as a result of property dangers such as a slippery walkway or an unmarked dangerous ledge.
Giving out an incorrect key probably does not rise to this level of harm since (thankfully) there was no assault or worse when the door opened.
These guidelines from the eNotes link below further indicate the kinds of things a hotel must do:
- Hotels are not liable for every accident or loss that occurs on the premises, nor do they insure the absolute safety of every guest.
- Hotels have a general duty to exercise "reasonable care" for the safety and security of their guests.
- Hotels have a general duty to reasonably protect guests from harm caused by other guests or non-guests.
- Hotels are not liable for harm to person or property unless "fault" can be established against the hotel.
- Hotels may be "vicariously liable" for the NEGLIGENCE of their employees.
The last two points are the most applicable to your situation. "Harm to person" might be difficult for you to prove, though certainly everyone would admit that the embarrassment would have been significant. While it is true that at least one employee made a terrible error in your situation, you may have trouble proving negligence in the legal sense.
It seems to me (and remember I am NOT a lawyer) that you have no legal recourse because you were not legally damaged; however, it certainly seems reasonable for you to expect some form of compensation, in the form of a free stay, a discount voucher, or whatever else might seem reasonable for that hotel and your circumstances. It is also your right to offer a critique of the hotel in any of the review sites (and perhaps even the hotel's own site) which documents your experience.