Trailing 12 (or more), which includes the last 12 months of rent roll, P&L - Profit and Loss statement, if possible the tax statement. Also, info about when the past renovations, what all were replaced (giving you an idea of the big ticket items coming your way).
Try stopping by the property and talk to a few tenants, this gives you an insight into actually living there. Try and talk to the maintenance staff, ask if they had unlimited budget what all would you do to the property? Trust me that question would reveal a lot things that you wouldn't have anticipated.
Call the reception and talk as if you want to enquire about a possible lease, will give you an insight into how the management company deals with customers (You might not even pickup the call, or respond to your voicemail mail). Do the same in person, see how they show you around.
These are just a few things you can start with and is no way an exhaustive list.