I've never personally run into any issues, but I know others who have. The thing is, people are well aware of the fake service dog scam, and some places are allowing associates to deny someone service if they think your dog is fake.
Also, real service dogs don't need tags or a vest. Infact, most people with disabilities who have real service dogs, don't use tags. You don't NEED proof. All you need to do is simply say "he/she is a service dog". You may get asked very simple questions like "Is this a service dog" and "what tasks does this dog perform". Answer the questions calmly and don't give them a reason to suspect you're hiding something, and you should be fine. It's very uncommon this day in age for legit service dogs to have tags, and the only time you see it is usually from people who want to point out that they have a service dog (I.E. those who are faking it and trying to hard to convince people their dog is legit). Having tags is basically the equivalent of walking around with a huge sign that says "PHONIE".