In addition to fiction, Wells also wrote science textbooks and articles (and a lot of other nonfiction books), all genres where the writer needs to be pretty objective. In most science textbooks, the author doesn't jump in to tell us how cool aerobic respiration is. (Though we think that would be fine, because aerobic respiration really is pretty cool.)
In The Invisible Man, Wells often keeps the narration objective, meaning that we hear from the narrator only what we would see and hear if we were there. In fact, the narrator often uses what we think of as journalistic prose: it's as if he has gone through the countryside, talked to these witnesses, and written up the story from those eyewitness accounts.
For instance, we get a line like this: "So much we know from what was heard at the time and from what was subsequently seen in the room" (7.5). This prose seems to reach its peak in Chapter 26. The Invisible Man beats Wicksteed to death, but "[w]e can know nothing of the details of the encounter" (26.6). Why? Because no one told us. The narrator could have made up the details, but he's a trusty reporter and only tells us what he knows to be true.
Bottom line: the objective narrator is just giving us the facts, which makes the story seem more believable. It's not just a tale that Wells is making up: it's the truth.
There are times when the narrator stops being objective and starts seeming more omniscient (that means he knows everything... not a bad gig). For instance, the narrator is able to read several people's thoughts. We hear that Mrs. Hall had thought about her upcoming argument with the stranger (7.7). We hear Kemp's impatience with the police coming to trap Griffin (24.2). And we hear Adye's contemplation of death (27.52). These are all thoughts that only an omniscient narrator could tell us. And this narrator isn't limiting himself to a few people – he seems able to pop into anyone's head.
How does this affect our reading? If the objective narrator makes the story seem more real, does an omniscient narrator make the story seem less real? We think so. But at the same time, the omniscient narrator does help us identify more with the characters since we get to hear their inner thoughts. Basically, there are pros and cons to every kind of narrative technique.
That brings us to our next point. The Invisible Man doesn't need the royal thought-reading treatment given to the other characters. Instead, The Invisible Man does something that Frankenstein does, too: it gives the monster a chance to speak for himself. In this case, Griffin takes over much of the narration from Chapter 19 to Chapter 23. All that we know about London, we know because he tells us.
On one hand, that raises lots of red flags – can we really trust this guy who seems like a total psychopath? On the other hand, thanks to his, um, psychopathy – because he no longer feels shame or guilt – maybe we can trust him to tell the truth about whom he robbed or killed.
In any case, the chapters where Griffin takes over narration of his story are a useful opportunity for us to try to see things from his side. (We hate this side. That's largely why we think of him as an antagonist.) It's interesting to hear his side of the story from the horse's mouth, without any comments from the peanut gallery (i.e. the narrator). Unfortunately, people don't always speak the truth about themselves (not Shmoop, of course), so even though he's telling us his story, there might still be something mysterious about the Invisible Man.