US permanent resident, Canadian passport.
US to Canada online check in (mobile) is no problem.
Canada to US online check in (mobile) does not work.
It asks for passport info, then asks for a return date. If you do not specify a return date it will not let you check in. I realize you could lie and specify a date, then it would probably work as mentioned before, but if you are being truthful and do not have a scheduled return date you cannot check in.
There was no place to enter green card info.
I find this ludicrous as I did not have to provide green card or return date while checking in at the airport. Although perhaps due to preclearance Delta doesn't bother to check as you aren't going to get very far if you don't have valid documents versus non preclearance where they would have to fly you back. So maybe not so ludicrous, but at least it should give you a check box for permanent residents of the destination country.