There was considerable dialogue between the sides for much of the 16th century. The separation between them was not, in the moment, a foregone conclusion, and many people continued to cherish hopes of reconciliation long past the point that, in the hindsight of five centuries, we may now think it was hopeless. Still, I suppose it depends on what you consider "public debate". Luther's 95 Theses were couched in terms of a formal academic disputation between scholars, and it's notable that the 95 Theses specifically were never given such a debate. However, the issues were discussed in pamphlets, such as Johann Eck's Obelisks and Luther's response Asterisks. Eck and Luther also debated in person at Leipzig in 1519.

Beyond that, there was the Diet of Augsburg in 1530, where the Reformers were called upon to make a confession of their faith, which they did in what is now called the Augsburg Confession. The papal theologians present wrote a response to it called the Confutation, and finally Philip Melanchthon, Luther's co-worker (maybe side-kick) wrote an Apology (or Defense) of the Augsburg Confession responding to the Confutation. This back-and-forth of Confession-Confutation-Apology would probably qualify as a debate on some of the major issues.

At this point, I can comment on the public's level of awareness of such issues. Luther's Small Catechism, intended for individuals and families, had been published a year or two previously, which was a big step in spreading his ideas. Also, there was controversy as to how open the Diet of Augsburg should be - the Roman side wanted it to be a closed-door meeting, to keep a lid on all these ideas. The reading was officially closed to the public... But it was a hot day, that June 25 in Augsburg, so the doors and windows were open for ventilation, and the man who read the Augsburg Confession out loud did so in as loud and carrying a voice as he could muster, so the people gathered around the building and the courtyard outside were said to have heard every word of it.

Following this, the position between Rome and Wittenberg continued to deteriorate. After Luther's death in 1546, the Holy Roman Emperor launched an attack against the Lutheran territories to try and bring them back into line by force, and he was successful on the battlefield. This led to the Augsburg and Leipzig Interims: the Augsburg Interim was the emperor's decree in 1548 ordering the Protestants back into theological agreement with the Roman church with little or no dialogue or concessions; the Leipzig Interim was basically Philip Melanchthon's counter-proposal, in which he was willing to re-adopt a lot of the outward ceremonies and appearances of the Roman rites as long as their churches were allowed to continue preaching what they believed was the Gospel doctrine. This won him many enemies in the Protestant camp, and there's still a subset of Lutherans today who kinda hate Melanchthon's guts. But one could definitely consider that an attempt at dialogue and compromise, giving ground on certain issues to preserve the most important central one to him.

Moving ahead, in 1561 there was the Colloquy of Poissy, a meeting between French Catholics and Huguenots (French Protestants). It was called by Catherine de Medici, the mother of King Charles IX of France, who at the time ruled France as the regent for her young son. In the preceding decades, the Huguenot movement in France had been growing increasingly influential; though relatively small in numbers, there were enough prominent and powerful Huguenots to cause unrest in the country. This was compounded by uneasy relations between French Catholics and the pope. Catherine was thoroughly ambivalent concerning the religious and doctrinal nature of the disputes, but nevertheless desired church unity in her country for reasons of political stability.

The Protestant side was led by a Calvinist, Theodore Beza, and in fact the idea was floated that the Catholic and Calvinists sides could compromise with the Lutheran Augsburg Confession - they recognized it as something of a middle ground, but neither was willing to budge enough to adopt it, so the Colloquy ultimately led to nothing, and throughout the late 16th and 17th centuries the Huguenots were pretty well crushed.

Finally, a notable later meeting between Lutherans and Catholics happened at the Colloquy of Worms in 1557. It was arranged by Ferdinand, who had recently succeeded his brother Charles as the Holy Roman Emperor, as yet another attempt at restoring religious unity and tranquility within the Empire.

The Lutheran delegation included many prominent theologians, such as Melanchthon, Brenz, Strigel, and Mörlin, as well as younger theologians at the time like Martin Chemnitz and Jakob Andreae. At the height of many of the controversies that would not be resolved until the Formula of Concord twenty years later, the differences between Philippists and Gnesio-Lutherans (the ones who hated Melanchthon's guts) were painfully obvious. Coming just a few short years following the Augsburg and Leipzig Interims, as well as the Religious Peace of Augsburg only two years before, the ecclesiastical climate was not one conducive to peace and reconciliation on any front. The Roman Catholic delegation quickly exploited the lack of agreement within the Lutheran camp, and the colloquy collapsed with the Lutheran theologians and princes thoroughly embarrassed.

Even concerning the Council of Trent, an invitation was extended for Lutheran representatives to attend. The general perception of Trent has been colored by the subsequent centuries and the turns historical events have taken; however, though the aim of Trent as a whole was indeed anti-Reformation in the sense that it was opposed to schism, it does not seem to have been absolutely inflexible. At least in the beginning, the Council was prepared to make concessions on the Lord’s Supper in both kinds and clerical marriage, just as the Augsburg Interim had done, had more Protestant cooperation been forthcoming.

Though Lutheran representatives were not allowed to participate in the proceedings, it seems that at least in 1551-52 there was some presence by Lutherans from multiple territories in the German lands, including Württemberg and Electoral Saxony. Even John Calvin wished to be present at the council, but was prevented from doing so by circumstances. Between their lack of satisfactory representation and the changing fortunes of war with Emperor Charles’ defeat in 1552 by Moritz of Saxony, Protestant participation quickly ended and nothing came of it in the council’s final results.

The issue that prevented meaningful Protestant involvement was not a lack of will to participate in debate over the matters, but questions of the authority and the freedom of the council itself. In 1546, several Lutheran theologians, including Bucer, Brenz, and Major, received an oral invitation via Melchior Flavius to attend Trent with a Papal promise of safe passage. Bucer’s response was that if the council declared itself superior to the Pope and would hold bishops to the pastoral standard of First Timothy, he would attend. This condescension not being forthcoming, the invitation came to nothing.