I don’t think it’s ok to monitor a spouse or even the children but that’s not the discussion.
A relationship is about trust. If you feel you don’t trust your spouse then monitoring will only make that problem worse, cause then you have accepted that situation. If your spouse has done something worth of loosing that trust, lying or deceiving you, I think talking about it is what you have to do. A relationship must be about honesty and openness. That doesn’t mean you have to share everything. I believe you need to have some private things.
Monitoring your spouse might feel like one way of relieve yourself from whatever you suspect him/her for and give you the answers without that person knowing you lost your trust in that person. That is deceiving your partner and that is committing more or less the same thing you suspect that person for.
When would you stop monitoring your partner? When are you satisfied with not finding something awful? In a week, month, year? Or will you stop when that person finds out? What happens when you find out your spouse has an internet friend that for a while is a vent, and sometimes talk about very personal things you don’t?
You might create a problem that didn’t exist before. And sometimes you make mistakes that you realize are mistakes, which could be blown out of proportions by being spied on.
I don’t think you should ever do something your spouse wouldn’t approve of. If your spouse feels the same way, you share a common respect for each other.