Buying rental with tenant

[Pandu Chimata]

There is an offer to purchase a rental property but it's coming with a tenant. The tenant seems to have signed eStoppel. It means the new buyer has to continue with that tenant. 

Other than obvious checks (such as inspecting lease agreement, payment history, tenant job history, etc.) what are some of the extra measures I should do to ensure I am not inheriting a problem?

Also, how the inspection of the house going to be accurate if the property is occupied? 

Thoughts?