It can damage the engine the same way a turbosystem can: Lean conditions, high EGTs. You can crack pistons and melt valves just the same as with a turbo.

All nitrous is is added oxygen, with a nitrogen buffer.. you could do the exact same thing with pure o2, albeit much more dangerously. Where a forced induction system actually forces more air into the combustion chamber, nitrous actually increases the amount of oxygen that is inducted. Anytime you add more oxygen, you have to add more fuel to compensate.. make sense?