I think that as long as the autopilot is able to fly in a crosswind or with an engine failure, it can probably land with one. Autopilots are already able to do these things.

I doubt anyone has tested this in depth, but I'm not sure there are too many configurations of airplane these days where a human can safely land it and a computer can't. Maybe if a big chunk of wing or control surfaces were totally gone, but even a human pilot isn't getting 99% reliability in a situation like that.

In any case, I don't think that the first candidates for automation are gonna be passenger flights. It will probably be small cargo planes first - Cessna Caravans and other turboprop aircraft where the cost of paying pilots is roughly similar to the price of fuel.