I'm reading Iron Kingdom and didn't fully grasp exactly what the causes were for that time to be tumultuous
There were two, somewhat separate, dissident movements in Vormärz Prussia (and they were only "dissident" and "movements" in a qualified sense). The first was largely in the Prussian core territories and enfolded up elements of the emerging Prussian middle class as well as intellectuals, those on the outskirts of the Prussian state, and various disaffected individuals and groups. Although the notion of a broad German national crusade against Napoleon in 1813 was largely a myth, this particular set of mythologies had great currency in post-1815 Central Europe. The idea of a nation taking up arms against a foreign invader was particularly strong in Prussia. Of all the German states in the 1813 campaign, Prussia had the most degree of mass mobilization and came closest to what nationalist mythology would enshrine as a people's war. The reforms of Stein and Hardenberg, aimed at streamlining and modernizing the Prussian state, ending ancien regime practices such as guilds and ending the last vestiges of serfdom. These reforms though had less to do with creating a more open Prussia and were more to do with restoring Prussian power after the calamitous defeats of 1806. Naturally, the Prussian state moved away from reformism after Waterloo and it adapted a much more conservative cultural policy. But the mythology of the Befreiungskrieg and notions that Prussia needed a constitution along with other improvements became rallying cries for a good many of Prussia's emerging middle classes. The reform period thus became shorn of its practical anti-Napoleonic character in this popular and politicized mythology and instead transformed into a move towards a more modern Prussia cut short by myopic East Elbian Junkers.
The other half of political dissidence in post-1815 Prussia was the Prussian Rhineland. This area had been given to Prussia by the Congress of Vienna partly as compensation for not having absorbed all of Saxony. The Rhineland was one of the areas of Central Europe that had been under French occupation the longest and there was a good deal of French institutions that Rhenish elites had "colonized" like the Napoleonic Code. There were other problems with this territory as well. The region was largely Catholic, which did not sit well with the mostly Protestant Prussia. Economically, the elites of the Rhineland were arguably more cosmopolitan and more geared towards commercial industry than the East Elbian Junkers elites. Hohenzollern methods of rule over the Rhineland also tended to appoint non-Rhenish and Protestant governors for the region. The Vormärz was characterized by attempts by Berlin to clamp down on suspected sedition while Rhenish elites sought to preserve their relative independence. One illustration of this precarious balance was that although Berlin could issue censorship decrees, Rhenish juries, still using the French Code, could acquit offenders. The Rhineland thus emerged as one of the regions of Prussia with a free-ish press. The young Karl Marx, for instance, made his name in Rhenish newspapers for his attacks on the existing political order and was twice acquitted by Rhenish juries.
Of course, not all of this disenchantment with the Prussian order was political. The nascent industrial economy and emerging interconnection between European economies contributed to unease and tensions. The Rhineland had benefited under Napoleon from "hothouse" protection of the Continental System, but now found it had to compete with other manufacturers. On the other end of Prussia, the textile industry went through a period of fitful growth that made it vulnerable to disruptions. As with the Rhineland, Silesia was more Catholic than the Prussian core territories and had a further ethnic dimension to it, as there was a strong Polish presence in the region. Industrialization created so-called "new men" whose status did not easily fit into the existing Prussian state apparatus and society. While the charter generation of industrialists and other new middle class professionals could make a modus vivendi with the Prussian state, their sons often had a much harder time of it. Elements of the younger generation found themselves gravitating to more radical ideas such as the Young Hegelians of Prussia's university system or nationalist ideas in student Burschenschaften of the growing German university system.
Dissatisfaction with the political order did culminate in sporadic revolts and barricades, but it was not until 1848 that a conjunction of factors aligned to lead to what proved to be an abortive revolution. Older historiography as well as popular memory has castigated 1848 as a "turning point that failed to turn," but the reality was the dissidents had very different aims and Weltanschauungs. Prussian liberals may have wanted a unified German state and a constitution guaranteed by the Hohenzollerns, while some Rhenish dissidents wanted either independence or a more radical restructuring of German society. The divided nature of the 1848ers was a reflection of the fact that political dissidence was quite incoherent in the Vormärz period. While it is very easy to tell what dissidents were against, what they were for was a different matter altogether.