Moisture will be your biggest problem. if you still want to do it though, run conduit so you can fish new cables through in the future.
keep power in a different receptacle than your data lines, even 110v/20a can mess up cat 5e and some cat 6 ethernet.
I would run HDMI and ethernet to your home router area assuming you have some device to feed the TV with such as a PS3, XBOX, XBMC.
Another option for making a cheap bathroom TV "Smart" is slapping an AppleTV or Roku to the back. then you have Netflix and some basic home served movie/video capabilities.
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Guns, and stuff. 
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