text "open" to such-and-such number [2]. The company managing the service will keep a short-term record of who's been pooping, so if anything unsavory (aside from last night's Mämmi) happens, the police will have the mobile number of the culprit.
Assuming the company protects their users' privacy (a non-trivial assumption, I admit), and assuming the mobile numbers aren't passed to telemarketers selling portable toilet seat covers, I see no problem in this approach. If people know they will be identified, they'll be less likely to cause trouble.
It's obviously not a foolproof system -- stolen mobiles will be a problem, as will friendly people who hold the door open for people waiting. But there's no such thing as a foolproof system. The goal should be to find the balance between privacy and security that maximizes the period between incidents of excretory malfeasance.
100% uptime can be guaranteed only if a) privacy is completely surrendered or b) society is fully assimilated into the bathroom utopia. Finland has made a good compromise: mostly secure, and mostly private. That's a bathroom I'm willing to poop in.