Recently a writer said that the good thing about first person was that you get to tell the truth. And I-- never one to let a categorical statement stand categorically-- riposted that it all depends, as it's the character's understanding of the truth, which might or might not be true.
I came across an example of this in Ian McEwan's Sweet Tooth, which is in first-person. The issue here isn't whether the POV character is deliberately or subconsciously distorting the truth, but one of certainty-- she doesn't know to a certainty:
My sight lines weren't good, but I thought his hands were shaking.
That is, she's confessing that she doesn't really know because of "the sight lines", but she's reporting what she thinks she sees. Of course, two considerations here:
First, the narrator WANTS his hands to be shaking, that is, that he's evincing nervousness at being close to her. (She wants to think he's attracted to her.) So her perception might be less than accurate, just because she wants it to be so.
Second, one step removed-- the author put this in there. If there was no relevance, if it didn't matter, then the author wouldn't have bothered. We as readers generally assume that whatever is narrated has some importance, whether or not that's the fact. And the author knows we'll think this is important, and so decides whether or not to include this based on whether or not he/she thinks it's worth getting the reader excited about these shaking hands.
So let's assume McEwan chose to put this in there because it had some (albeit perhaps slight) meaning. What are we to make of it? Is it actually true (the character's hands really are shaking)? Or is what he wants us to get is that the young lady watching wants him to be nervous, thereby showing us that she really does like him (despite her recent rejection of him)?
That is, is the "importance" the event (hands shaking) or the POV's perception (her thinking that his hands are shaking)? The fun of this is, of course, that we don't need to determine that at this point in the narrative. We can wait to find out if he's really that affected by being near her, or if she's just hoping that he is.
Now think about how differently that simple observation would be rendered in the more common form of third-person. There would be no doubt, because ordinary third-person narrates what's happening.
His hands were shaking.
We wouldn't need the line about the sight lines, because this would be a narration of the action of the scene, not the narration from her perspective about what she's thinking as the scene plays out. In ordinary third-person, we are given no reason to doubt the truth of the narration. Clearly this is the POV of choice if you just want the reader focusing on what's happening, if you don't want them wasting time doubting or speculating. His hands were shaking. Nuff said.
But what about Deep Third POV, which is cognitively much more akin to first-person, in that narration is completely through the perspective of a character (though with third person pronouns -- he/she)?
In that case, the perspective-limiting observation (sight lines) and the doubt would probably be preserved.
Serena's sight lines weren't good, but she thought his hands were shaking.
A deep third narration is no more certain than a first-person narration-- both are colored and perhaps distorted by the limitations, desires, and biases of the POV character.
So, short work of it:
If you don't want the reader speculating, common third is your best choice. This would be more useful in plot-driven books, where the characters' inner workings and doubts aren't that important.
If you want the reader speculating and doubting if the character POV is transparent and accurate, use first-person or deep third. That is more appropriate for character-driven books.
Examples? I'd love to start collecting some examples.