Property management companies do owe fiduciary duties in most states, which is a higher standard than ordinary negligence. This means they must act in your best interest, disclose conflicts, and exercise reasonable care.
Key evidence to gather: (1) the management agreement (look for scope of duties, standard of care, termination provisions), (2) communication logs showing you raised concerns, (3) maintenance request records, (4) financial statements showing what they charged vs. what was actually done, (5) comparable management fees to show their fee wasn't a bargain that might excuse reduced service.
One common gotcha: many management agreements have mandatory arbitration clauses. Check yours before filing suit. Also check for attorney fee shifting provisions — they can cut both ways.