A most interesting question!
There are some studies surveying bacterial flora in aquarium fish with a view to assessing zoonotic risks, but they are few and far between. In particular have a look at Trust & Bartlet 1974 (Appied Microbiology) or Shotts et al. (1976) (J. Fish Res. Bd. Can.). I believe both studies were for freshwater fish and water samples. I did recent search for similar studies on marine fish studies but didn't find much. If you turn up anything, I would be most grateful for the reference (s). While many bacteria genera were represented in samples for these two studies, serious zoonotic pathogens were not readily evident. The most common bacteria isolated were Gram negative species of Pseudomonas, Aeromonas and Citrobacter. Although, some other genus/species were isolated that could cause infections in people. The results are a little confusing and as expected given that fish are living things that do not come from sterile environments! You need to read the papers to come to your own conclusions, however. It is worth noting that Mycobacterium spp. was not found, although a couple acid-fast colonies were noted in some samples. This is agreement with Eric's comments that Mycobacterium is rare (at least in freshwater fish). Both studies suggest that while the risk from zoonotic infection from aquarium fish is low, further study is warranted and contact with fish should be avoided to minimise the potential for infection. This should be a critical consideration as any aquarium should be located behind a wall to prevent access by the public for the safety of the public - and the fish. In this regard, I would be more concerned about risks from physical injury than from infections agents (and why the tank needs to be in a secure location). By eliminating contact with the water you essentially ameliorate the risk of contacting an infection. In reading all this, it seems to me that given high risk hospitals represent for nosocomial infections (i.e. infections originating in a hospital from people) - an aquarium would be the least of their worries! I agree with Eric that the benefits of having an aquarium in a public area as a way to reduce stress in a potentially stressful situation, especially for kids, far outweigh the minuscule risk from picking up an infection. I too have been to many doctors and dentists' offices where aquariums are present and strongly feel that people really do enjoy, and benefit from, the calming effect.