It depends on the superhero and the nature of their superspeed.
Superheroes who have superhuman reflexes:
- might only interfere with events that occur right next to them, since their speed is limited to their ability to move short distances. This would include most martial artists (Batman, Lady Shiva, Bronze Tiger) combat masters (Captain America, The Taskmaster) or limited speedsters such as Triathlon (3x the reaction speed of a normal human).
- They may also not live in an enhanced state requiring some sort of power-up before their superspeed is available.
Example: Bronze Tiger is out walking his mastiff and a foul ball from a nearby playground escapes the playground and is about to hit a small child. Being a good distance away, he spots a nearby soccer ball, and with his enhanced reflexes and martial skills he blocks the errant baseball with a well placed kick of the soccer ball. No one is sure where the soccer ball came from and Bronze Tiger continues his quiet afternoon.
Heroes with Superspeed who are not speedsters:
- Will likely only use their superspeed to do the bare minimum required and likely never without being already dressed for the occasion. (Superman, Wonder Woman, Gladiator, Silver Surfer)
- The exception might be the non-speedster who is fast enough to be relatively invisible and not cause catastrophic effects from using their super-speed.
Example: Superman may be moving through a neighborhood on his way to a fire. He sees a gunman about to shoot a policeman. He disarms the gunman, at superspeed, so the gun simply disappears from the gunman's hands. The former gunman is promptly arrested. Superman does not stop and all that is seen is the resultant gust of wind from his passage. But if he is in Metropolis, everyone knows what just happened.
- Heroes who have superspeed that can be used without destroying the environment as a side effect of their powers may be the most likely to use their speed to perform "invisible" rescues when they have the time and interest to do so. (Almost any Flash from the DC Universe is able to use superspeed without major environmental effects due to their "speed/friction aura.")
- It might be difficult for them to know when to stop, or there may be a threshold to how much can be done for any particular set of events. See: Can the Flash see the future now?
- Even a speedster has a finite amount of time, energy and focus available to monitor their surroundings so they will likely be focused on the issues that bring the greatest reward to the greatest number.
Example: DC Comics took this idea to a horrifying extreme in the Kingdom Come series when the Flash, in an effort to keep everyone in Keystone City safe, uses his power to patrol at superhuman speeds, a nonstop force for justice, preventing crime and accidents though out the entire city, living between the ticks of a second.
From Kingdom Come, The Flash protects Keystone City at superspeed, non-stop.