And you can go on title as a tenant in common with your mom - as long as her % TIC ownership is enough to absorb her reinvestment requirements. 

Under the Howey Test, a transaction is an investment contract if:It is an investment of moneyThere is an expectation of profits from the investmentThe investment of money is in a common enterpriseAny profit comes from the efforts of a promoter or third party

For example, if they presumably want to make improvements to their new investment, improving common areas, etc., can they / are they likely to force through a special assessment that will apply to all owners, through the HOA board that I'm sure they'll control?

Written inventory of all furnishings and other personal property in, on, or commonly in use for the normal operation and maintenance of the subject property.

Be aware that some of the common overlapping expenses cannot be deducted.

@Ben Joseph the proper policy is you need is a Non Owner Occupied Rental Dwelling policy, commonly know as a Landlord policy.You are correct in a Rental Dwelling policy will usually have Liability as part of the policy.

They are 4 bedroom, 4 bath, and they share the common spaces.

The title company has a form that the buyer's fill out saying how they want to take title such as as an unmarried person, as joint tenants, as a married person as separate property, as tenants in common. 

INDEMNIFICATION: The Owner shall indemnify and hold harmless  Property Managemer  from and against claims, demands, losses, costs, damages, actions, suits, or proceedings (hereinafter called "claims"), by third parties that arise out of, or are attributable to, the Property Manager's performance of the agreement provided such claims are:1. attributable to bodily injury, sickness, disease, or death, or to injury to or destruction oftangible property, and;2. caused by negligent acts or omissions of the Property Manager or anyone for whose acts the Property Manager may be liable.

Increased vacancy and expenses (common for properties I buy) would certainly impact the property value.Unfortunately, I've found that sometimes I've overpaid for a property because I overlooked some serious maintenance/capex/tenant issues, and I haven't been able to correct them in the year purchased.