Based on the simple assumptions he made, Copernicus correctly deduced:

• the correct "picture" for the size of the Solar System
• the correct explanation for retrograde motion.
• the explanation for the phases^*, variable brightnesses, and sizes of the planets.

• ....

Despite all of the above successes, the Copernican model was not embraced for sound scientific reasons:

• the model did not explain the observations any better than did the Ptolemaic model; Copernicus was forced to introduce epicycles to be even be competitive with Ptolemy because of his assumption of uniform motion on circles
• he simply stated that the stars were very far away in order to explain the lack of an observed annual trigonometric parallax
• there was no physical foundation for the model

^*The Phases of Mercury and Venus weren't observed at the time. Their discovery awaited Galileo and the telescope.