1. to verify initially whether or not there is infidelity involved in your sitch, so that you can attack it appropriately.
2. to establish evidence/grounds for a possible divorce action if yours is a "fault" state.
3. to gather evidence for a possible custody battle, and to help you make a determination as to whether or not you SHOULD go for custody (is the cheating spouse engaging in risky behavior that would make them a poor parent in their current state).
4. to determine what it is that OM/OW is providing your spouse, so that you may begin to better provide it. To determine what OM/OW is doing that ticks your spouse off, so that you can avoid those behaviors.
5. as an early warning system for any possible financial or legal threats.
6. to monitor what outside pressures are having an affect on your spouse (her parents, her friends, your adult children, etc.).
7. to determine if the affair has gotten physical (medical risk).
8. to verify no-contact once no-contact and transparency have been agreed to as part of reconciliation.
9. to determine the extent to which you believe OM/OW may be a risk to your spouse and/or your family (ex.: abuse, unstable behavior, etc.).
10. to expose deceitful tactics of the cheating spouse which, if unverified, may lead you to make false assumptions and tactical errors (ex.: cheating spouse says they want to go to MC to try to work on reconciling the marriage, but they confide to a BF that they are only doing it to buy time while they squirrel away marital assets to be used on a divorce).
Those are some "pro's" just off the top of my head.
On the "con" side, all I can come up with is:
1. If you don't control your emotions, you may not be able to handle it.
I'm sorry, this whole "snooping is BAD!" thing, to me, is just one of those mantras that gets mindlessly repeated, until it becomes part of the official catechism, without stopping to consider the real merits of it.