Copernicus’ mathematics: No essential difference from that used by Ptolemy: Crude algebra, with no convenient notational system, elementary trigonometry (tables of chords). This turned out to be a genuine restriction. With appropriate mathematics, Copernicus might well have done more.
Epicycles remained, just as in Ptolemy’s system.
Copernicus managed to remove the equants, but only by substituting equally ad hoc centers of rotation (the sun was not the center of rotation).
Copernicus’ lunar theory (using a double-epicycle) was a clear improvement over that of Ptolemy.
One of the advantages of the heliocentric theory which could have been understood and known by Copernicus’ contemporaries was its ability to explain the variations in brightness of planets (such as Mars), and the phases of the inner planets (Mercury and especially Venus).
The disadvantages of the Copernican system–from the point of view of the 16th-century reader–included, among others:
There should be observable annual parallax in any heliocentric system, yet none was detected (until 1838).
Loss of Earth’s unique central position (of theological concern).
By Aristotelian principles–and there was no replacement as yet for Aristotle– the heliocentric theory complicated rather than simplified celestial physics. The motion of the heavy Earth had now to be explained. This would involve new concepts of space, time, matter, cause and, arguably, a transformation of the eternal verities, a new set of relations between Man – Nature – God.