Mug shots are rarely flattering, and there is also an argument to be made that releasing them publicly (like requiring suspects to do a "perp walk") infringes to some extent on a suspect's right to be considered innocent until proven guilty. What really isn't in dispute, though, is that an unflattering mug shot is not an emergency situation that should be reported via 911.
The Smoking Gun (which does love a good mug shot) reported recently that a Georgia woman had been arrested and charged with unlawful use of 911 after she called to complain about the quality of a previous mug shot. The woman had seen the photo on the cover of "Bad & Busted," a local publication that reproduces such things, and according to the police report she called 911 to report that "she was upset about how she looked on the front page of the Bad and Busted printing." The officer stated that he informed the woman that 911 was for "emergencies, injuries, or violence," not requests for retouching.
That didn't stop her from calling 911 again later that day to say that she "needed a place to keep her bags." Important, maybe, but still not an emergency. She did get a place to keep her bags, namely the trunk of a squad car, and also got an opportunity to have a new mug shot taken. The Smoking Gun says the one it's now displaying is the most recent one, and if that's an improvement then I guess it's understandable why she wasn't happy with the first one.
Previously in Needless 911: sandwich not to caller's liking, caller wishes to report hookers' breach of contract, callers report they are lost in a corn maze, caller states McDonald's has run out of McNuggets.