Power has changed hands many times in Star Wars, but perhaps the least effective governing body is the New Republic. This alliance of systems was supposed to usher in an age of peace and prosperity after the Galactic Empire's tyranny. That's not exactly what happened, though.
As recent Expanded Universe tales reveal, the New Republic fell down on the job. Not only were its members negligent in establishing themselves as a unified body, but they failed to learn from history. Their utter lack of common sense led to the Empire's resurgence in the form of First Order, leading to the events of the Star Wars sequel trilogy. The New Republic had all advantages, and they completely dropped the ball.
5 Demilitarization
Following the Galactic Civil War, Mon Mothma and several Rebel figures advocated for downgrading and even disbanding their armies. As a result, the New Republic had minimal military power. One might think this reinforced its peaceful goals, in an attempt to learn from the past. After all, the Old Republic's own army of clones became a weapon against its own citizens and helped usher in the Empire. However, this was a case of learning the wrong lessons.
Having no standing army meant that the New Republic had no way to back up its authority. As a result, it couldn't enforce the laws or defend against threats, be they foreign or domestic. Such a flimsy foundation is naive at best and disastrous at worst.
4 Lack Of Awareness
Out of sight, out of mind. Not only did the New Republic not enforce laws within its own territory, but it seemed utterly uninterested in the space beyond. Whenever pilots reported suspicious activity in the Outer Rim, the higher-ups either ignored it or didn't follow up. That's assuming the pilots reported it at all.
This is shortsighted in more ways than one. Most importantly, such blindness made the New Republic vulnerable. It's understandable that the heroes didn't want to rule the outlying planets. However, real-life countries are at least aware of what their distant neighbors are doing. That way, they can prepare for any potential threat, either through diplomacy or force. As it is, the New Republic purposely left a massive blind spot. Its members were practically asking to be invaded.
3 Putting The Resistance Out To Pasture
This goes hand-in-hand with the military mistake. At first glance, the Resistance seems like the official army of the New Republic, but that's not the case. It's actually a private militia established by Leia. The New Republic acknowledged and tolerated this group, but they were not formally affiliated. This distance did more harm than good.
Namely, it placed both parties in an awkward position. Having a rogue army running around undermined the New Republic's policy of peace, law, and order. Suspicions that the government was funding this army made its members look corrupt. On the flip side, the Resistance didn't have the funding or authority it needed to accomplish its goals. The lack of commitment ultimately allowed the First Order to flourish in the shadows, and it's all because the New Republic wanted to have its cake and eat it, too.
2 Letting Mas Amedda Go Free
Not only does this guy look like the Devil, but he directly answers to the Star Wars equivalent of such a figure. Mas Amedda served as the Grand Vizier to Chancellor Palpatine, also known as Darth Sidious. He remained the villain's right-hand man throughout his rule, even after the birth of the Empire. As such, he was privy to many of Palpatine's dark dealings. That goes not just for politics, but also his activities as a Sith Lord.
After his master's death, Amedda surrendered on behalf of the Empire. At that point, the Rebels should have thrown him in the slammer. Instead, they returned him to power, and Amedda became the head of the provisional government on Coruscant. Granted, he was little more than a puppet ruler. Plus, Coruscant was no longer the Republic capitol. However, he was still complicit in countless appalling crimes: helping the Emperor conduct his evil plans and selling his propaganda to the public.
Amedda didn't deserve any power, provisional or otherwise. He probably still harbored the temptation of that power. Putting him back on the street — especially in a political position — was asking for trouble. With that platform, he could subtly influence others to adopt the Imperial cause. He had intimate knowledge of Palpatine's manipulation, after all, so he may have picked up a few things. Using that knowledge would make Amedda a huge thorn in the New Republic's side.
1 Letting The First Order Flourish
Without a doubt, the New Republic's greatest mistake was leaving this business unfinished. The Rebels may have defeated the Empire, but that doesn't mean that the Imperials magically vanished. Millions of troops, officers, facilities, and sympathizers remained across the galaxy. It was more than enough to start again, and start again they did.
The Imperial remnants eventually formed the First Order. What makes this worse is that the New Republic could have easily avoided this result. The Rebels should have hunted the Empire's members down and apprehended them. Most of these people were guilty of war crimes, so they deserved justice. Their countless victims would certainly agree. Not only would this be a fitting demonstration of the new governmental body, but it would have discouraged attempts at regrouping, mainly by limiting their numbers. The Allies didn't leave the Axis to flourish after World War II; they put parameters in place to maintain the peace. The New Republic should have followed that example.