The heliocentric 'theory' is not really a theory at all, more an assertion that the Sun is at the centre of the solar system. Copernicus's theory assumes that the Sun is at the centre and provides a model of the planets' orbits that uses circles and epicycles to explain the observed orbits. He said it was simpler than the old "geocentric" (Earth centred) Ptolemaic system, but it was not really, it actually had more epicycles. Note: Perhaps the questioner got mixed up. The Copernican theory IS a heliocentric theory. Perhaps the question is about the geocentric theory and the Copernican theory. Anyway, Kepler simplified the heliocentric theory and now we know that his model is correct.
There are far more than five scientific errors. The Geocentric theory for instance
He developed a better geocentric model than the one that was made before it
His theory like the Aristotelean epicycles theory assumed motions were based on circles. Thus even though his theory was simpler than Aristotle's his predictions did not agree as well with measurement. It was not until Kepler changed the circles to ellipses that Copernicus's theory gave predictions that agreed better with measurement than Aristotle's theory did that it was finally easy to accept the Copernican sun centered system.
most scientist believe in the heliocentric more than the geocentric
They showed that it's possible for an astronomical object to orbit around something other than the Earth, so it was a first step in dismantling the geocentric theory. On it is own this did not prove anything but with further discoveries from about 1670 onwards the heliocentric theory started to take root.
“An ounce of experience is better than a ton of theory simply because it is only in experience that theory has vital and verifiable significance.”
Galieo was the first scientist to study the night sky systematically with a telescope. One of the things he discovered was the phases of Venus, which had not been seen before. In a telescope Venus looks like a crescent when it passes between the Earth and Sun, for a few weeks either side of its closest approach to Earth, called inferior conjunction, when it is invisible (in line with the Sun approximately). That was consistent with the old geocentric theory that placed the Earth at the centre of everything. Galileo also discovered that when Venus is near its furthest point, superior conjunction, it shows a gibbous phase (like the Moon between half-moon and full moon). That is not explained by the geocentric theory called the Ptolemaic system, that had lasted for 1500 years, because it shows that Venus in this part of its orbit is further away from us than the Sun, which is impossible in the Ptolemaic system. Galileo used this as a proof of Copernicus's heliocentric theory, but he was mistaken in this because Tycho Brahe had produced a geocentric theory that still had the Earth at the centre, but allowed Venus to pass behind the Sun (as seen from Earth). It needed many further discoveries after the time of Galileo to make people realise that the heliocentric concept is the correct one. The modern system uses Kepler's model. Kepler used the Copernican idea of having the Sun at the centre, but threw out the circles and epicycles of the Copernican theory. In the modern theory based on Kepler's laws, each planet is in an elliptical orbit with the Sun occupying one focus.