I love seeing dogs in stores. Sometimes it irks me that only little dogs can get away with it. But I recognize that for jealousy, since I'd never own one of those self-motivated bedroom slippers. I prefer a DOG dog.
As for the dog crapping in the store... seriously, people do it too. I'd rather clean up dog crap than human crap. No shit.
From a legal perspective, I'll concede the health code issues in grocery stores and restaurants. But I don't think it's a reasonable restriction. In Europe you can take your dog anywhere, and you know what? People aren't dropping dead in droves from dog-vectored diseases spread through the neighborhood cafe. I get really excited when I see people sitting at an outdoor cafe with dogs in attendance. (In most states with which I'm familiar, dogs can be at outdoor venues, such as porch seating at a restaurant.)
As PPs here have already expounded upon, the allergy issue is bunk. I know a guy who is so allergic to cats that he would break out in hives when he went into a co-worker's office, because of the dander on that man's coat. Do you propose that people who own cats shouldn't go out in public? I, too, react nastily to perfumes, even those in laundry detergents and such. I'd love it if people would stop wearing that crap. I'd rather smell BO than Chanel No. 5. But I don't think it's reasonable to attempt to outlaw wearing them in public. I could go on with more examples, food related and otherwise; but others have already pointed that out.