One thing that it does is add suspense. Because we only get things through Montag's point of view, we don't know what really happened to Clarisse. We have to rely on information from other characters. Mildred claims she was hit by a car; Beatty alludes to the fact that she had died, but we really don't know for sure. So there is that suspense. Also, Beatty becomes a much more suspenseful character; we have to take him at his word for things, and it is a bit tense. He is more enigmatic and dangerous character because we don't know his entire story; we're not entirely sure how he is going to react to things. Also, we don't know Mildred's mind; for all we know, she could overdose at any minute. Not knowing leaves that situation quite tense. So, the limited 3rd person narrator adds more suspense.
It is also a great way to tell the story more realistically. We don't walk around every day knowing everything. We don't know the entire background and thoughts of everyone we meet. Bradbury's novel is more realistic because we only get one person's point of view-this is just like our every day lives. And as a result, it is more human, emotional, dynamic, unsure, and dramatic-more like real life than a huge, all-knowing omniscient perspective might have been.
Those are just a couple ideas to get you started. Good luck!