WARNING: The following contains spoilers for the Dragon Ball Super manga, by Akira Toriyama, Toyotarou, Caleb Cook, and Brandon Bovia, available now in English through Viz Media.
The Galactic Patrol, introduced in Dragon Ball Super, has been policing the Milky Way Galaxy of Universe Seven for over 10 million years, which is longer than Grand Zeno's reign over the Multiverse. The cosmic police force is led by the Galactic King as they maintain law and order throughout the galaxy. Though Jaco is the only recurring member, his incompetence at, well, everything, doesn't accurately reflect the rest of the Galactic Patrol.
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The Galactic Patrol operates from an enormous space station that serves as their headquarters. Their officers receive spaceships, standard-issue blasters and jet packs to allow them to fly, as none of them possess ki. Patrol members even have a weapon called an Extinction Bomb, which can wipe out all life on any given planet, though they thankfully prefer not to use it.
Even though their jurisdiction is limited to the Milky Way, that's where most of the action in Universe Seven takes place anyway. While some members of the Galactic Patrol are stronger than others, they are closer to the lower end of Dragon Ball's immense power scale. Outnumbered by the Frieza Force and outmatched by Frieza himself, the Galactic Patrol had little choice but to let the evil tyrant do as he pleased, resulting in his destructive conquest of the galaxy.
The Galactic Patrol doesn't fight battles that it can't win, often they'll recruit more powerful fighters to aid them. This is not to say the Galactic Patrol is helpless, considering they were able to contain Moro for over 10 million years after the Supreme Kai of that era had stripped the evil wizard of his magic. It's to the organization's credit that they'll seek outside help rather than futilely attempt to solve major problems or just ignore them entirely.
Whenever they are outmatched, the Galactic Patrol will try to inhibit their enemies in more minor ways. For example, they were unable to combat the Saiyan army, so they would send officers after Saiyan infants who were jettisoned to weaker planets to take them over. In fact, Jaco was dispatched to deal with Goku when he was sent to Earth as a child. However, Jaco got sidetracked and never found Goku, so when no Giant Ape ever tore up the planet, Jaco reported his mission as a success and went on his way.
The Galactic Patrol is surprisingly bureaucratic, given how often Jaco complains about paperwork and worries about getting credit for an arrest, whether he deserves it or not. They don't even allow outsiders to fight alongside them unless they formally, albeit temporarily, join the Galactic Patrol. Goku and Vegeta, as well as the rest of the Z Warriors, were forced to wear a Galactic Patrol insignia on their clothing during the battle against Moro.
Given the massive size of their jurisdiction, the Galactic Patrol is oddly narrow-minded in their view of the cosmos. Even after they worked alongside a Supreme Kai, they refused to believe that Lord Beerus actually existed until Jaco met him. Yet, like the gods, they view time travel as a taboo and a crime. However, if it's something like Hit's Time-Skip or Whis' Temporal Do-Over, which can't result in a branched timeline, they will look the other way.
Other than Merus, who was revealed to be an Angel-in-training, Galactic Patrol members find themselves generally outmatched by powerful villains. Yet, the Galactic Patrol appears to do a surprisingly good job policing the galaxy. After all, they've only had three culprits they couldn't handle: Frieza, Majin Buu and Moro. Granted, these incidents resulted in the deaths of untold millions, but statistically, only three failures in 10 million years is an unbelievably high success rate.