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Emily is correct when she says that sheds can affect property values in a negative way. But I also think they can increase property values when they are designed and built well.
I dont think the sheds themselves attract rodents. Its really the things inside that can attract them. So if you have food or water in your shed then you shouldnt be surprised when you open your shed door to a bunch of rats.
In my opinion sheds are great and they can look absolutely gorgeous when done right. But your HOA board should come up with strict controls so that the shed building and designing doesnt get out of hand. I would also suggest requiring owners to maintain their own sheds by a certain standard (keep them clean, no chipping paints, no deformities, etc)