No it is totally against ethics and law. You can not spy on anyone. And if your landlord is saying for this then ask him why would I do it? It is not your job to abide by his dictations. Say him clearly that you can not do this.

 The landlord can ask--you don't have to accept. If a condition is placed on the request--"I need you to watch them or I'll have to evict you", then there's a problem. It's unrealistic to expect you to watch all the time--it's not your job, it's his. But if you notice them moving, why not let him know? It never hurts to have your landlord appreciate you (he'll remember it if you're a few days late with the rent, maybe).