I live in New England and am interested in having a permanent spot in Montreal. Are there real estate agents in US who could help me? Or is it best to work with a Montreal-based realtor? What are the pit-falls, and tricky details in all this? Or is it better to rent?

I suggest you find a local (Montreal) agent that deals with international clients. Call around and find one that works with "business" people that live and work in different cities. It is very common in most large cities for people to do this. I wouldn’t use an agent from New England unless they live part-time in Montreal.