It is widely believed that the Ptolemaic research program had become "degenerative" when Copernicus wrote. The claim is that Ptolemaic astronomers kept adding more epicycles. That they were un-knowingly attempting to test the unfalsifiable hypothesis that a curve could be approximated with enough circles.
The author of the Wikipedia article to which I linked yesterday (who seems very very
Epicycles on epicycles
According to one school of thought in the history of astronomy, minor imperfections in the original Ptolemaic system were discovered through observations accumulated over time. It was mistakenly believed that more levels of epicycles (circles within circles) were added to the models to match more accurately the observed planetary motions. The multiplication of epicycles is believed to have led to a nearly unworkable system by the 16th century, and that Copernicus created his heliocentric system in order to simplify the Ptolemaic astronomy of his day, thus succeeding in drastically reducing the number of circles.
With better observations additional epicycles and eccentrics were used to represent the newly observed phenomena till in the later Middle Ages the universe became a 'Sphere/With Centric and Eccentric scribbled o'er,/Cycle and Epicycle, Orb in Orb'-- 
As a measure of complexity, the number of circles is given as 80 for Ptolemy, versus a mere 34 for Copernicus. The highest number appeared in the Encyclopaedia Britannica on Astronomy during the 1960s, in a discussion of King Alfonso X of Castile's interest in astronomy during the 13th century. (Alfonso is credited with commissioning the Alfonsine Tables.)
By this time each planet had been provided with from 40 to 60 epicycles to represent after a fashion its complex movement among the stars. Amazed at the difficulty of the project, Alfonso is credited with the remark that had he been present at the Creation he might have given excellent advice. 
As it turns out, a major difficulty with this epicycles-on-epicycles theory is that historians examining books on Ptolemaic astronomy from the Middle Ages and the Renaissance have found absolutely no trace of multiple epicycles being used for each planet. The Alfonsine Tables, for instance, were apparently computed using Ptolemy's original unadorned methods.
16) Owen Gingerich, The Book Nobody Read, Walker, 2004, page 57.
Owen Gingerich does not appear to be a fringe figure in the study of the History of Science
Owen Gingerich is Professor Emeritus of Astronomy and of the History of Science at Harvard University and a senior astronomer emeritus at the Smithsonian Astrophysical Observatory. In 1992-93 he chaired Harvard's History of Science Department.
I n the past decades Professor Gingerich has become a leading authority on the 17th- century German astronomer Johannes Kepler and on Nicholas Copernicus, the 16th- century cosmologist who proposed the heliocentric system. The Harvard-Smithsonian astronomer undertook a three-decade-long personal survey of Copernicus' great book De revolutionibus, examining over 580 sixteenth-century copies in libraries scattered throughout Europe and North America, as well as those in China, Japan, and Australia. His annotated census of these books was published in 2002 as a 434-page monograph. In recognition of these studies he was awarded the Polish government's Order of Merit in 1981, and subsequently an asteroid was named in his honor. An account of his Copernican adventures, The Book Nobody Read, is in fourteen foreign editions.
Professor Gingerich has been vice president of the American Philosophical Society (America's oldest scientific academy) and he has served as chairman of the US National Committee of the International Astronomical Union. He has been a councilor of the American Astronomical Society, and he helped organize its Historical Astronomy Division. In 2000 he won the Division’s Doggett Prize for his contributions to the history of astronomy. The AAS awarded him their Education Prize for 2004. He has also won the most prestigious award of the French Astronomical Society, their Prix Janssen 2006.
The day before yesterday, I had a totally false belief. I thought that( *after* Ptolemy, later Ptolemaic astronomers introduced cycles which were not centered on the Earth (the planets going on epicycles around those cycles -- I now know that the center of such cycles were called eccentrics) and, more importantly, allowed a rate of motion around that cycle which was not constant either as observed from the earth or from the center of the cycle. Rather it was constant if seen from another point called an "equant"*.
I was wrong. Ptolemy introduced both eccentrics and equants in the mid 2nd century AD. This means that they were not recent fudge factors. They were ancient fudge factors which were about 1400 years old when Copernicus published.
The author of the Wikipedia article (who cites Owen Gingerich) asserts that there is no evidence supporting the claim that Ptolemaic astronemers added epicycles within epicycles in the middle ages and rennaissance. He claims that Ptolomy's model with no modifications was in use at least in the 13th century.
This model was accurate to within about 1 degree when Ptolemy introduced it (IIRC, and who knows if I do, Ptolemy explicitly said that he was aiming to predict to within one diameter of the moon which is, not coincidentally almost exactly one degree (and presumably the reason we measure angles in degrees with just a bit of rounding to the nice 360 degrees per full circle).
As far as I understand from the Wikipedia article to which I linked yesterday (unedited but convincing) Ptolomy's model was working fine about 1350 years out of sample.
Claudius Ptolemy refined the deferent/epicycle concept and introduced the equant as a mechanism for accounting for velocity variations in the motions of the planets. The empirical methodology he developed proved to be extraordinarily accurate for its day and was still in use at the time of Copernicus and Kepler.
Owen Gingerich describes a planetary conjunction that occurred in 1504 that was apparently observed by Copernicus. In notes bound with his copy of the Alfonsine Tables, Copernicus commented that "Mars surpasses the numbers by more than two degrees. Saturn is surpassed by the numbers by one and a half degrees." Using modern computer programs, Gingerich discovered that, at the time of the conjunction, Saturn indeed lagged behind the tables by a degree and a half and Mars led the predictions by nearly two degrees. Moreover, he found that Ptolemy's predictions for Jupiter at the same time were quite accurate. Copernicus and his contemporaries were therefore using Ptolemy's methods and finding them trustworthy well over a thousand years after Ptolemy's original work was published.
Now if economists' problem is that other economists had added fudge factors 1400 years ago, the claim that economics is not dominated by a degenerative research program might be as strong as, but no stronger than, the claim tht Ptolemaic astronomy was not a degenerative research program.
This is actually also related to Brad's thoughts on undergraduate teaching. He thinks it is useful to teach the history of thought. My high school physics course involved some of that. The idea is that people remember history mixed with the other subject better than either alone. My post below was written from memory of a high school course I took in 1976 (or maybe a book I read in 1982). I believe I correctly recalled Copernicus's principle objection to Ptolemy correctly, although I thought he had more trouble with eccentrics than he did (I won't read what I wrote so I don't know if I wrote my claim clearly).
As I recalled correctly, Copernicus had no propblem with epicycles (his model had epicycles) but did not accept equants (I also thought he hated eccentrics). Indeed
The equant violated the stricture of perfect circular motion, and this violation bothered thinkers a good deal more. Thus, in De Revolutionibus (see Copernican System), Copernicus tells the reader that it was his aim to rid the models of heavenly motions of this monstrous construction.
(same link as Ptolemy introduced ...)
Thus Copernicus's explanation of his reason for rejecting the Ptolemaic model is completely different from contemporary explanations. Also, on the point of disagreement which Copernicus considered crucial, modern astronomers more nearly agree with Ptolomy than with Copernicus. He was right about the center of the solar system, but, in a disagreement of Ptolemy and Aristotle Copernicus agreed with Aristotle and modern astronomers agree with Ptolemy.
Modern astronomers believe that the center of the orbit of the planets is not the center of the Sun (the Sun is at a focus, the center of an ellipse is halfway between the foci) *and* that the planet moves faster when near the sun so the degrees of motion per day (or second) are most nearly constant if measured from another point which is further from the Sun than the center of the orbit is). This corresponds almost exactly to an eccentric and an equant as used by Ptolemy.