What exactly would you like to do with the information if you had dead proof of the affair?

I'm asking because it's important to think this through.

Would you want it so you could confront him and break through the lies? Would you then be okay with it if that drove him to separate and be with her? Or are you fantasizing that this would be the thing that starts him to repair the marriage? It can go either way, you shouldn't confront him unless you are okay with either outcome.

Would you like to know for sure for YOU, so you can stop second guessing yourself and make a decision for your life based on the truth? Then go ahead and hire a private detective. I know I wouldn't be able to stand being in that position and not knowing.

Would you leave him if you knew for SURE? Are you in a position to leave (or to boot him) or should you be shoring up your financial situation first? Think carefully about your financial plans before you upset the applecart, I say. You might need to squirrel away an emergency fund, or plan to split the joint accounts the day you tell him, or might need to obtain financial records first before you boot him.

Or you might be one of those people who plans to DB and be positive and hope he drifts back from the affair - in which case, knowing more details about the affair will only drive you crazy. Pictures and love notes especially - don't look at them if you don't want to be haunted by them.