I just wrote out a reply and then my browser crashed when I clicked send. So I'll keep my thoughts brief:
Indris have bred after being relocated to near-semi-captivity, so maybe captive breeding (if ethically justified) isn't so far off.
As Maguari mentions, tarsiers are kept in several Asian institutions, and several keep them on permanent display. They do breed in captivity and several US zoos have briefly kept them in the past.
Giant armadillo are frequently kept in a few South American zoos. I'm not sure about their current situation but Colombia's bioparque los ocarros tries to keep them on permanent display and has had reasonable success in their husbandry. Roque Sáenz Peña zoo in Argentina is another one which holds them every now and then.
Only about 5-6 dugongs are kept in captivity in Japan, Singapore, Indonesia and Australia. I'm not sure if any interested Chinese/Korean facilities have managed to get hold of any yet.
We're lucky to have a great variety of experts here on zoochat, and there are already a few threads by very knowledgeable people on Javan rhino conservation. I think that ultimately they're not as 'evolutionarily distinct' as Sumatran rhinos, and that their numbers are a bit more stable. As far as I'm aware, there are currently none in captivity.
I don't think there are officially any captive dingiso. Occasionally members of other 'new' tree kangaroo species pop into captivity, e.g. tenkile. Tim Flannery's book, 'Throwim Way Leg' gives brilliant accounts on his discovery of the dingiso and several other species. I can't remember exactly which Dendrolagus species he mentions were kept as captive specimens by local villagers.
I don't really have anything to add to the information about leopard seals and platypus, but you might find the forums an interesting read.
A lot of research is being carried out on the live display of deep-sea creatures, particularly in Japan where the Imperial Family have had a great interest in marine biology (the current Emperor, Akihito, has published ichthyological articles). A new exhibit at the Oceanopolis in France is also encouraging:
BBC News - 'Abyss Box' to keep deep animals