Another thing that it is really important to pay attention to in first-person writing is what that character knows. Not what he/she knows about the plot; that should be obvious. About everything else.
When your first-person narrator looks at the street outside his house, does he see Fords and Chryslers and Saturns? Or does he see red vans and silver cars and a blue pickup? In other words, is he the sort of person who knows all the makes and models and maybe even the year, or are they just all cars to him? When she sits on a rock under a tree, does she notice that it’s metamorphic limestone and a fine specimen of Acer saccharum, some kind of unpolished marble boulder and a sugar maple, or just a rock and a tree?
In a third-person viewpoint, the writer can fudge the narrative a bit even if she’s doing a tight third-person point of view, and let the reader know that it’s a sugar maple even if the viewpoint character has no clue. In first-person, you can’t fudge. If the viewpoint character says “I sat under a sugar maple,” then obviously she knows it’s a sugar maple.
This seems like a small thing, but it can come around and bite you when you least expect it. You have your viewpoint character describe a tree or a car or a horse in specific terms, because you know what it is and you want the reader to get a clear picture of the scene…and then four or five chapters later, the character says he doesn’t know the difference between an oak and an elm, or a Saturn and a Lexus, and any reader who’s at all noticing goes “hey, wait a minute, he used to know that…” Or worse yet, you turn out to need him to know (or not-know) something as part of a major plot-point. If it’s first-person, the only thing to do is go back through everything and hope you catch every place where you might possibly have said something in the narrative that indicated differently.
Of course, this can work to your advantage, too. If the first-person narrator describes elms and sugar maples by name, but just “red cars” and “blue cars,” then when the plot requires him to not be able to identify the robbers’ getaway car, he doesn’t have to say that he can’t tell one car from another. It’s already there, in the word choices he’s made every time a car came up in the narrative.
Furthermore, this cuts both ways with the worldbuilding as well as the characterization, especially if you’re a fantasy or science fiction author writing in a completely imaginary world. The reader builds up a picture of the world from what the narrator says, and how she/he says it. In first person, you have to be a little more careful, because the reader can’t tell whether the first-person narrator is omitting details about the trees because they’re unimportant and/or the same as in our world, or whether she just doesn’t know what sort of tree it is. Yet you can also use things like the way the narrator takes purple carrots for granted, or thinks of lemon-flavored streams as rather commonplace, to tell the reader things about the world that are a lot trickier to get across in third person.
In fact, one of the things that is, for me, the most fun about writing first person is that the narrator can have attitude. Her opinions about people and things don’t have to be implied or shown; she can just say them straight out. “I hate pickled beets.” “Donald is stupid.” Because of this, though, first-person is almost inherently unreliable. That is, the reader is predisposed to believe what the first-person narrator says, so if the narrator lies or doesn’t know what she’s talking about, it’s a lot harder to let the reader know that she really does like pickled beets and is just grousing, or that Donald actually could have been a rocket scientist if he’d wanted to.
Every type of viewpoint has advantages and disadvantages like this, and eventually, I’ll probably get through most of them.