Under the ADA, staff can ask two questions about the "service animal" (defined as "...a dog that is individually trained to do work or perform tasks for a person with a disability":
(1) is the dog a service animal required because of a disability, and
(2) what work or task has the dog been trained to perform (i.e., it can't just sit there and "be" an emotional support animal... it has to do something).
But then:
"This definition (of "service animal") does not affect or limit the broader definition of ... “service animal” under the Air Carrier Access Act.
See, e.g.,
http://www.ada.gov/service_animals_2010.htm
Wish the ACAA was more specific regarding service animals and the identification of such. I also personally think other passengers, as private individuals, should call out fake service animals themselves. Nothing in the ADA or ACAA prevents that from happening.