I'm interested in purchasing a run down old apartment building with intent to ultimately demo the structure and rebuild for other purposes. The building currently has 8-10 small apartments leased. I have not seen any of the current lease agreements. What should I be looking out for and what is the feasibility of getting them to all move out so I would be able to demo?

you'll want to know what the lease agreements say.

1. Let the leases expire and not renew. Could take up to a year depending on when the last person signed.
2. Let the month-to-month's expire. Pay off the rest depending on how many months are left in their lease. Need to make sure all tenants agree before handing over cash.

Only additional thought I would have is whether any of the tenants are LMI, voucher, Section 8, etc. If so, then I would also make sure there are no use restrictions in place. For instance, if someone received a loan from HUD or housing improvement assistance (disaster recovery, HOME programs, etc) then there could be restrictions lasting up to 10 years. Seller should disclose, but depending where you are in process it may not have come up.