I mostly agree, but I'd argue that epicycles actually made useful and testable predictions, although we found a simpler description later on. The article underlines a lack of refutable theories. Thus, I think [1] is a better analogy.
The characteristic of metaphorical epicycles is that the make simple, testable predictions that are then wrong, which are fixed with another epicycle.
Another more subtle aspect of epicycles, real ones this time, is that they are too powerful and can be used to prove anything. You can predict the motion of the planets with epicycles, it's just that the required series is very long or infinite. And with very long series of cycles, you can "predict" anything: https://youtu.be/QVuU2YCwHjw?t=25s Thus, one of the problems with epicycles both real and metaphorical is that they are indeed not refutable. Because epicycles can predict anything, they aren't that useful; they exclude far less than meets the eye at first.
It isn't hard to see that characterist showing up in string theory. The theory has for a very long time had problems with excluding possibilities, and each new metaphorical "epicycle" seems to come with more parameters than the last, rather than fewer. Now, this isn't unique to string theory since all the current theories seem to have that problem, but then, the point is, why does this problematic theory have so much more support and money than the other problematic theories?
>Another more subtle aspect of epicycles, real ones this time, is that they are too powerful and can be used to prove anything.
String theorists talk about how rich and complex the mathematics is, but maybe that just means it has so many possibilities you can always come up with an explanation to overcome newly-discovered difficulties.
Well that's really all that is wrong with it: you are adding epicycles instead of working on a better theory. In analogy: once a language is turing complete you can do anything in it, so you can keep using brainfuck to make a gui, but probably it would be easier in java...
[1] http://rationalwiki.org/wiki/The_Dragon_in_My_Garage