To lease or not to lease... that is the question

I have a mobile home park with leases that I inherited from the previous owner. Many of the leases are not even executed (signed) as I believe they were manufactured for the file. The fact of the matter is that the tenants are all paying the correct rent every month so they know they have a lease of some sort. Should I leave well enough alone, or should I have each tenant sign a new lease? What are the advantages or disadvantages to doing so?