Optimates and the Populares. The influx of wealth and slaves from conquest disproportionately benefited the wealthy while the common people lost their farms and tradesmen lost work to slaves. As the need for reform became ever more pressing, the Optimates dug in their heels, using the Senate as a roadblock to any reform legislation. Their stubborn adherence to this tactic and refusal to compromise is what finally provided the incentive for reformers to break precedent.

The Gracchi brothers began the unraveling by using the tribune's veto to block all legislation, standing for office for successive terms, and proposing legislation. None of these acts was illegal per se, they were just violations of generally accepted rules. In response, the Optimates introduced their own unfortunate precedent: retaliatory violence. Once the conflict broke into the open in such ways, the system became more perverted. Roman soldiers no longer needed property to join the legions, becoming more loyal to their commanders than the state. Marius, with the backing of loyal soldiers, became consul seven times. He and Sulla marched on Rome with armies, purging each other's followers.

A victorious Sulla tried to bring back the conservative regime by creating the cursus honorum, but no amount of law could undo the example he and Sulla had set by attaining power through violence. The First Triumvirate finally managed to circumvent the Senate without retaliation by pooling their wealth, political, and military strength. The Republic was practically dead at that point. When the Senate declared Caesar an enemy of Rome and he crossed the Rubicon in 49 BC, his action was no longer shocking because the precedent of violence had been so firmly established.

One strength of the Roman Republic that eventually helped it grow into an empire was its military structure. The Roman militia operated on a sense of duty and honor that made soldiers loyal to their deaths. It was highly organized and featured comparably advanced technology that allowed Rome to win many battles and wars. The larger the Roman Republic grew, the more adept their army became at capturing new lands and integrating them into the Republic.

A weakness was the almost constant corruption in the political structure. Although the Republic operated with elected officials, many of these officials had bought themselves into office through bribery. This bribery continued once they were elected, as many officials voted based on who gave them the most money. This also led to an imbalance in representation, as the majority of officials were wealthy upper-class Romans.

Strengths and weaknesses are matters of opinion, and people who have different political beliefs will likely have vastly different ideas of what constitutes strength and weakness in any government. From a democratic viewpoint, however, the strengths and weaknesses of the Roman Republic government amount to a rift between theory and practice.

One strength of the Roman Republic was that it recognized the right to citizenship. A weakness, however, was that not all citizens enjoyed equal rights. The socio-political structure of Rome was sharply divided along class lines, with rights granted or restricted based on socioeconomic status.

Another strength of the Roman Republic was that it recognized the need for a decisive authority, namely, a Senate. The weakness was that the Senate was composed solely of aristocratic men, and after a period of violent protest, the Senate was stripped of its power and authority.

A third strength of the Roman Republic was that it recognized the importance of equality. The Romans wrote down laws on stone tablets, and those laws guaranteed equality for all citizens. The weakness of the laws was that the exclusive nature of citizenship promoted inequality.

The Roman Republic had a system of checks and balances, which can be considered another strength and which in theory ensured the survival of the best ideas from oligarchy, monarchy, and democracy. A weakness, however, was that the government was controlled by the ruling elite. This made a balance of power impossible.

One of the strongest features of the Roman republic was its very definition of the principle of republicanism.  In representing a government where elected officials are meant to represent the will of the body politic proved to be a lasting legacy to all governments that followed the Romans.  The United States Constitution used the Roman Republic as an example of leadership and the principle of republicanism was something embedded into the minds and hearts of the framers.  I think that one of the weaknesses of such a system ended up becoming what happens when the citizens' needs are not met by representative government.  Essentially, what redress is there when a government committed to the nature of the people's wishes are not fully embodied by said government?  This becomes a critical issue and something that helped to destabilize the Roman government.  It is also a reality that all representative governments must address, and in the process, one that helps to define the essence of how different principles of government must work with one another to prevent the weaknesses of one being exposed and making the government a crippled one.

During its time, the Roman military was one of the strongest in the world. By the 3rd Century CE, it had helped the Roman Empire conquer most of the known world. It had defeated a number of strong enemies, such as the Carthaginians. However, it was unable to fend off the barbarian tribes that eventually brought about the end of the empire. Let's look at some of the strengths and weaknesses of the Roman military.

Strengths

One of the biggest advantages that the Roman military had was its size. Recruitment during the period of the Punic Wars and the early Imperial period was massive. Italy tended to supply the elite soldiers of the Praetorian Guard, but the colonies and Romanized provinces supplied the rank and file of the army. In many of its conquests, the Romans were able to put a large number of soldiers in the field and outnumber their enemy.

Roman soldiers were also very experienced. Rome employed a professional army where soldiers served for decades. This meant that they were well trained and battle-hardened. Unlike civilian armies, Roman soldiers were ready to fight on the battlefield without the need to spend time training and mobilizing.

Being a professional fighting force, the Roman army was able to employ advanced battle tactics. The legion formation required the training and discipline of professional soldiers. This tight and coordinated battle technique was easily able to defeat enemy armies that were unused to such coordinated fighting.

The versatility of the weapons of the Roman army was another strength. They were able to employ the latest in military technology to their advantage. Heavy weapons such as ballistas and trebuchets were useful in sieges. They knew how to use long-range javelins and short gladiī depending on what the battle plan called for.

Weakness

The Roman army was never really able to develop its cavalry. The Roman cavalry remained a relatively weak auxiliary fighting force throughout its history. It was never able to contend with the cavalry of their Persian enemies.

At various times throughout the history of Rome, military leaders were politicians and aristocrats looking to add a feather to their cap. They were not always seasoned and knowledgeable military commanders. These amateur commanders stumbled into a number of embarrassing defeats. Most notable was Varus, who lost three entire legions fighting the German tribes in 9CE.

By the 4th and 5th Centuries, recruitment had become a problem. The army just was not big enough to defend such a large empire. To fill the gap the Romans began using more barbarian mercenaries in their ranks. This coupled with the declining quality of equipment greatly weakened the Roman military by the empire's end.

This question likely refers to the whole history of Rome from 8th B.C.E to the 5th century C.E. despite the reference to the Empire that existed from the time of Augustus to the Barbarian invasions in the West and even longer in the eastern Roman (Byzantine) Empire. To this end, it is better to have more information, especially as each phase of Roman civilization (monarchy, republic, monarchy) transitioned from from the last, creating very gradual changes.

Some strengths of Rome were its military power. Not only was Rome's professional army unique at its height, their tactics and commanders were second to none. The various legions of the Roman army were loyal to Rome and not their commanders, so the fight for their civilization and way of life gave them a tenacious fighting determination. Close range weapons (gladius) worked in tandem with the shields and spears designed for long range disruption of enemy formation. Romans also learned from their enemies, be it the development of ships in the First Punic War or how to counter the threat of Hannibal's war elephants in the Second at Zama.

Romans were also skilled administrators, building the roads and communication tools that were necessary if they were to have large areas of land under the control of one people. Even though Rome largely expanded due to the threat of enemies all around their borders (which naturally persisted as the Empire expanded and during periods of shoddy Emperors), their systems were effective to the point that it would take more than a powerful enemy to bring them down. It is almost a boring answer, but Rome more destroyed itself through internal problems than it was outright conquered. Their enemies merely noticed and took advantage, as a system can only persist if the people are dedicated to it. Apathy is the real weakness in the fall of many an empire.

Other weaknesses included power too concentrated in the Senate and later the Emperor. While consolidation of power works with benevolent leaders who serve the public rather than their own ambition (Cincinnatus) it was rarely the case with the patrician class, what with the wealthy Roman senators serving their political ambitions rather than the good of Rome, the ability for few to climb the cursus honorum, and the flagrant violations of the rules designed to hold ambition in check (ie: no repeated holdings of offices; longer term limits) in the final generation of the Roman Republic. During the specific Empire period, there was also the choosing of Emperors by the Praetorian Guard, which caused short and often chaotic reigns, as these guards' favoritism would wax and wane, especially as they were the military presence within the city of Rome during this time. This made administration difficult and brought the notice of the enemies of Rome.