Are there any examples (real life cases) of invalid FMS data affecting flight operations?
Here is some old material used in Europe to prepare for the transition from AIS to AIM: AIS to AIM: Enabling the Net-Centric Information Environment by Roderick van Dam, Head of Eurocontrol Legal Service. The document references two legal cases where navigational data and hardware were involved.

Pakistan International Airlines


  Bejon v. Pakistan International  Airlines (Toulouse Court of 
  Appeal, 1998) Liability of Jeppesen raised.  Jeppesen argued that
  approach map  was based on map provided by States.  Court concluded
  that map was  technically acceptable This case confirmed  the risk
  related to  the publication of Aeronautical data.


More: PIA Flight 268.

American Airlines


  American Airlines v. Jeppesen- Anderson and Honeywell (US Federal 
  Court, 2000) The Accident Report had concluded: the probable causes
  of the accident were  related to failures of  the flight crew; 
  contributing factor was related to FMS-generated navigational
  information; AA blamed the Jeppesen software in the  Honeywell
  computer; alleged that products  helped caused the crash; A Federal
  Jury found  that Jeppesen was  17% at fault and Honeywell 8 % at
  fault.


More: American Airlines Flight 965.