akriss do you have any idea how ridiculous that sounds? If at any point you are arrested for public-pissing I think you must necessarily re-evaluate more than your law school chances. I know the circumstances are somewhat mitigating, but there surely must have been a porta-potty in the vicinity given the nature of the setting.
Akriss, I don't know how the case will affect your applications, but don't listen to the people on this board who think the fact that you peed outside (which most human beings do) means that you have to reevaluate your career choices.
Seeing as your arrest was recent I would say this bodes poorly for you. I also think contesting the claims might POSSIBLY be viewed in a negative light - law schools tend to like repentance (and learning!) in addition to distance (and maturation).
I don't think it bodes poorly for you, but I think you should just plead guilty to the Public Intoxication and see if you can get your lawyer to bump the "Outraging Public Decency" charge down to Public Urination, if there is such a thing. You really can never fight Public Intoxication charges - it's almost always up to the discretion of the officer what that means, so that you are liable to be prosecuted for it anytime you step out of your home slightly buzzed.
Ask your lawyer about it. Tell him your priority is not just "getting off the hook" but having the best result for your law school applications. These goals are different.