Its at no more risk with a decent dyno operator than it is on the road - just think of the way some twats thrash their car from stone cold, yet they keep going. Prolonged dyno time can have issues with heat build up, on turbo cars especially. Just make sure your tyres are in good condition inflated to the correct pressure.
As for how reliable, thats very subjective. Different brands tend to give different results, so many different factors - ambient temp & humidity, tyre pressures, the way the car is running etc etc. There is lots of BS about it. The truest figure they can give you is the measured power at the wheels - they might also give you a flywheel figure (e.g. 225bhp for an LCR), but unless they take the engine out of the car and bench test it, this will be a estimated figure, calculated using figures to represent loss through the transmission. So comparing results with someone who got their car done on a different RR on a different day can lead to a few arguments.
What dyno time is very good for is perfecting your car there and then. Making sure the fueling is right throughout the rev range - not too rich, not too lean. Making sure there are no holes in the fueling gives a dip in the power/torque curves. It will highlight component failure too.
