Often when I have to stay in a hotel that is not dog friendly with my service dog I am asked to sign a damage contract - they cannot charge a pet fee for a service dog, but if the dog creates damage the handler is responsible for that.
My dog went to one of those "bijillion" dollar service dog training centers for about a year and is them re-created every 3 years. That, however, is not required by ADA and those training. Enters will give you a certificate of training. Omelet ion, but it is not required.
Any agency, store, or facility can "eject" a misbehaving dog - makes sense -- then why can't they eject the kid that screams there way through their whole shopping event
There are many suttle thing that a formally trained service dog will have, but certainly they are not always totally necessary -- example at training programs they teach the handler and the dog behaviors to keep them from getting poisoned- that is something that might be hard to show Target (which I have demonstrated to the store manager at one point).
But then I know people with drivers licenses who shouldn't have them