Standard for document in diagrams the power of motor
No, using an 800 kW motor on a machine that only loads it to 500 kW will make things run very much cooler which is usually a good thing (The motor will (steady state) only draw power equal to the mechanical load plus losses), but the over sized motor will:


Run cooler, and therefore last longer all other things being equal. 
Potentially have higher starting torque (and starting current), you will need to allow for this in your motor starting arrangements, should not be a big deal if running from a VFD, might be if doing something old school.
Have a lower winding resistance, hence a potentially higher locked rotor current, again an issue for protection design more then anything else.
Possibly have a slightly worse power factor when run at 500 kW, so you might have to deal with a little higher kVA number when sizing wiring and controls. 


However, when dealing with the thick end one of a MVA of power, probably at 11 kV or so I would not be listening to some random person on the internet, seek professional advice, this stuff takes no prisoners.