As the characters of "Finding Nemo" are amazingly close to reality, I was wondering whether the fish which was portrayed as "Dory" in the film actually has a short term memory loss problem in reality?
No, Blue Tang fish do not have worse memory than any other fish. Even gold fish can be trained and remember food routes for months, as seen on MythBusters, disproving the common saying of "goldfish memory".
Remember, Dory only says her bad memory runs in her family. Like Finding Nemo revolved around a fish disabled by birth defect/physical trauma, Finding Dory revolves around someone disabled with mental issues from birth. But it's not trait shared by the entire species, just Dory's lineage. Or at least she thinks it does.
The parents were going to have the Short Memory Loss as well, but it was hard to make it work. http://www.cinemablend.com/news/1524850/the-finding-dory-plot-detail-that-had-to-be-dropped-and-why Obviously the film shows that not even her parents have it. Only Dory has it. A single Blue Tang, not species wide.
My answer just scientifically complements @cde's answer. As it is longer than a comment, I'm adding as a separate answer.
The three-second memory is a myth
The fish Dory is based on does not have short-term memory loss. It is rather more awesome than that.
blue tang, regal tang and surgeonfish. Its scientific name is Paracanthurus hepatus.It has several names, including royal
And, the memory of fishes are much better than we think.
Like other fish, the royal blue tang is unlikely to have a bad short-term memory. There are no studies to suggest any fish has a "three-second memory". In fact, the opposite is true.
Fish can remember things for many months. One team of researchers discovered that carp could learn to associate a certain sound with food, and then remember it up to 5 months later.
Fish can even be trained to respond to visual illusions. This requires repeated training sessions so that they easily recognise certain shapes and environments. No one has specifically studied the memory of the royal blue tang. But given that several fish species have good memory skills, we should expect that Dory and all her relatives will be just as good.
I've made my answer spoiler-free for the "Finding Dory" film. But, the article (mentioned underneath as source) may contain some subtle spoilers.