Hell, you can even point your own domain at mailinator, so blacklisting will never work. Sorry.
Can't you just check the MX-record of the domain. If that point to mailinator.com (or the same ip as mailinator.com) you know that it is mailinator's domain.
Sure. And don't forget to check the A record if there's no MX. At some point it's probably not worth the effort, though.
I can set the MX to whatever I want during the validation stage. Then tomorrow, when I no longer want your email, I can point it back at mailinator.