The best use case I've seen so far isn't in currency transactions (not sure many properties are going to start accepting rent payments in Bitcoin anytime soon), but rather using the Blockchain technology to facilitate instant data transfer/sync across multiple vendor databases.
Once a record gets updated in a property management software system, Blockchain technology could have it instantly synchronized across all connected vendor systems (credit approvals, multiple accounting systems, CRM, resident portal, access management, whatever you can and want to connect to the network) – distributed ledgers have enormous potential in an accounting-heavy industry like multifamily.