In a purely technical sense the issue would be the structure of observations and conclusions drawn from those observations which would comprise the central issue of any resolution between the predictive side of astronomy and the demonstrative or interpretative side of astronomy.

It is true that the Galileo affair brought out the issue of Biblical interpretation using apparent motions against factual actual motions which ultimately created this science vs religion environment however this important issue tends to disguise problems which all sides were unsure of and,in truth, couldn't be dealt with until late in the last century or this century.

Everything from the current messes surrounding planetary definition, ignorance of the leap day as it serves planetary dynamics and their traits, climate change and all sorts of modeling/predicting is wrapped up in the technical issues nobody ,at least those of any relevance, wants to deal with or are content to leave historical characters as figurines acting out ideologies to suit present agendas whether it is attacking denominational Christianity or promoting voodoo and junk under the name of astronomy.

The issues should be fascinating for anyone who looks to astronomy beyond astrophotography or 'stargazers' as they call themselves but I haven't seen anyone come close to what is necessary to deal with refreshing astronomy as a pursuit that encompasses other sciences.