Commiting adultery does not prevent one from performing the duties you were trained and paid for. Getting pregnant does. Yes, there is a double standard.
True, but it is against the UCMJ, and when one is willing to ignore one or more laws, chances are they won't have problems ignoring others (which can affect your duties).
It can create a situation where if it is somebody higher up in the chain, those underneath may not feel the need to follow the rules/laws. I'd bet some have tried to use Clinton's behavior as Commander-in-Chief to justify their transgressions.
It can also impact unit cohesion if it involves people/spouses inside of the same unit (especially if it's a mixing of officers/enlisted).
I'm an old fuddy-duddy when it comes to this thing - I believe if you would break your wedding vows, then you would have no problems breaking any oath or rules you don't care about.