I had a great history Professor back in college. IANAH, but life-long novice student of it. Today, I posted his comment I remembered from my class on European history about The Holy Roman Empire, and posted it to a map of The HRE in /r/mapporn. This has lead to downvotes. I am asking here how accurate that statement by my Professor was.
The professor in question was spinning off a joke that Voltaire made in 1761. There are several layers to examine behind Voltaire's quip. Firstly, when Voltaire made that quip in 1761, the HRE was an institution that was floundering politically. Even to its contemporaries, the Reich was a curious institution and it governed itself according to a complicated patchwork of rules and regulations. The HRE was less of an empire in the formal definition of the word and was something approaching a confederation of multiple polities ranging from free cities to principates and bishroprics. One of the dominant traits of the post Treaty of Westphalia was that the HRE structures like the military Kreise and its overlapping legal systems served to protect the sovereignty and independence of the smaller entities. The rise of Prussia had severely undermined the integrity of this collective system as one of the HRE's larger components could now challenge the great powers and the Habsburgs on their own. The eighteenth-century growth in the strength of the state and marshaling of its resources meant that the structures of collective defense were no longer as viable as they were in 1648. By the late eighteenth century, it was clear that the Reich's institutions were not functioning and the question of how to reform the Reich was one of the dominant ideas in Central European discourse. For a man of Voltaire's generation, the inability of the HRE to function as a viable entity underscored the gap between reality and the pretenses of its political culture.
Another layer to Voltaire's quip is that as a French paladin of the Enlightenment, the HRE seemed to be an archaic relic of the past. The joke was part of a wider disdain Voltaire had for Central European culture and its various institutions. Although he was something of a court intellectual for Frederick the Great, he often joked in private to his friends about his patron's Francophillia, for example, calling correcting the French in Frederick's writing as doing another load of laundry for the king. Central European intellectual thought was often focused upon a somewhat lofty and weighty matters of philosophy and metaphysics, which Voltaire's books often satirized. The pretentious and absurd Pangloss in Candide was a thinly-drawn caricature of the German philosopher Gottfried Wilhelm Leibniz and Pangloss's excessive theorizing was Voltaire's snide dismissal of Central European intellectual culture. Within this context, the "neither holy,.." quip was part of a larger disdain Voltaire had for Central European pretensions and attachment to creaky structures that were seemingly irrelevant to world of the Enlightenment.
But for historians studying the HRE, Voltaire's famous quip that it was "neither holy, nor Roman, nor an empire," while catchy, obscures analysis of the HRE because neither its political culture nor Reich structures had really abandoned these ideas and often interpreted them in a way that cannot be reduced down to their fundamental definition of Holy, Roman, or Empire. For example, the Peace of Westphalia had cemented the idea that confessional choices fell under the purview the local states' rulers (cuius regio, eius religio) which led to a great seal of state sponsorship of theology and forms of religious expression. Whether in the Pietist theology produced in University of Halle or the various Catholic ecclesiastical music produced in the Archbishopric of Salzburg, the HRE was arguably at the forefront in European Christian thought and expression in the eighteenth century, so in that sense, it was rather "holy," at least compared to its contemporaries. While the HRE's connection to Rome was somewhat tenuous, it was one of the oldest polities in Europe and thus did have the closest connection to Rome. And "Empire" is often a slippery term as are issues of political centralization. Historiography in the nineteenth century took centralization as a given and after German unification, the Prussian-dominated academy tended to treat the HRE as a barrier to progress and the national principle. This dismissive attitude towards the Reich gave Voltaire's quip a new life and it is almost a cliche in older scholarship on Central Europe. Current scholars on the HRE as exemplified Peter Wilson and Joachim Whaley have emphasized that despite its many problems, the HRE was a less of a joke than even its contemporaries would admit.