As an RA, I feel your pain. I've been asked to show my green card on several occasions to board a flight to Canada and in Canadian Immigration.

He will need a green card to enter back to the US. Even by car, I'm pretty sure you are still required to show drivers liscense and birth certificate at a minimum. I've heard of them not asking for the birth certificate, but if your father has an accent, the agents will probably ask for further identification.

That being said, my green card expired last year and I had to travel to YUL before my replacement arrived. I showed my expired card and paperwork that I had submitted renewal, had interview scheduled, etc. and didn't have an issue. The passport with visa entry may be enough, but is still a risk.
I also travelled internationally back when you had to mail in your original card and my renewal hadn't arrived. I had to go to Dept of Immigration (at the time) and get a stamp but didn't have an issue returning. Not sure if that's the same stamp he has. However, this was a number of years ago and times have changed.

The border between Canada and the US isn't as strict as it could be. Based on my experience, he should be okay. If he does decide to travel, just be sure to arrive at the airport very early in case he has to go through a secondary interview.