I got pulled over for an expired registration and the registration was up to date. Can he still continue the traffic stop?

What do you mean by continue the traffic stop? He pulled you over to check the registration, it's up to date - then what happened?

The car was a rental and had rental plates witch means that it has permanent tags on it, can he pull me over?

If he thinks there is something illegal going on, yes, he can pull you over. That's what the Police do.

Probable cause for what? Did a search follow? Was contraband or other evidence of a crime discovered subsequent to the stop?

If he ran the places, or if the date sticker on the plates was not correct, rental cars still have date stickers on them, he can pull you over. And then you show them the rental paper work to prove car is proper.

I am guessing they found something else?