"Person of Interest" was great from the start and has only improved with time. Fans of the show are fortunate it has gained in popularity. Many shows never get a chance. They are canceled just as they are starting to get really good. "Person of Interest" was already pretty good and got really great, really fast. Now that the show has been renewed, it can get even better.
Renewal means the "Person of Interest" story arc can be expanded
By the end of Season 1, "Person of Interest" will likely have a large base of addicted fans. The fan base is already sizable, but with a mind-blowing season finale, a good portion of that large fan base may become rabid about the show.
A large base of true blue fans would mean that the writers would be able to add to the overall story arc without the worry of not being able to capture new fans who don't understand what's going on. In addition, it may be easier to gain some new fans who would take the time to watch from the beginning if they know it will pay off.
One important thing to note, however, is that the writers will have to create a stellar Season 2 premiere if they hook fans with an amazing Season 1 finale. They can't cop out on any cliffhangers. They can't have fans feeling let down all of a sudden. That will destroy any progress made almost immediately.
The "Person of Interest" renewal means the writers can get even more creative
The show is already very creative, but now they have a little more leeway. With another whole season of episodes, they can show us what kind of ideas they are really capable of, within reason. We want to see great creativity within the "Person of Interest" world already established. We don't want to see a ghost episode or an alien encounter.
Season 2 of "Person of Interest" can't skimp on the action for the sake of the story
Fans have come to expect a certain level of action from the show. Even if the story arc is expanded, and the stories get more creative, the level of action needs to stay the same. It could even be increased a bit. Action scenes do not necessarily take away from a great story, as long as they make sense within it.
The most important thing to note here is that fans of the show may start to drop off if they feel the show has become boring. A evolving story line keeps us captivated and hooked on the show, but a nice level of action keeps us from falling asleep before the end of the hour.