In order to answer this question, we need to go back to 133 B.C. This was when Tiberius Gracchus was murdered for seeking to redistribute land by circumventing the senate as a tribune of the plebs. Simply put, Tiberius and his brother wanted to redistribute wealth to help landless Romans. This was a watershed moment that divided Roman politics.
Some people sided with the Gracchi and others sided with the senate. Of course, this is a simplified version, but this framework offers a lot of milage. After the Gracchi Roman politics was fractured and many civil wars took place: Marius (of the people) vs. Sulla (of the senate) and Caesar (of the people) vs. Pompey (of the senate).
So, by the time of Octavian violence in Rome was rampant. In fact, Andrew Lintott, a very good scholar, wrote a book on this very topic. His appendix is filled with instances of violence in the streets of Rome.
What also compounded this atmosphere is that soldiers became more loyal to certain generals than to the state. So, people like Caesar and Pompey could wield very loyal and powerful armies. Finally, men began to take many offices all at once. For example, Caesar was simultaneously Pontifex Maximus, consul, and dictator in perpetuity.
In light of all of these events, civil discord followed.
Finally, as for whether there was political dysfunction, I would say yes. The Republic got too big not to change. The Roman people outgrew the political constitution of Rome. An empire needed an emperor and his staff.