Thanks for the great responses, everyone (especially the above two, wow).
I had everything internal until I realized I shift characters sometimes throughout the story. It's not like Chapter 1 is Character A and Chapter 2 is Character B, though - there is one main MAIN character and occasional breaks to see things happening in another place. Example:
SolVanderlyn was posting on the GAF writing thread, and he was immensely pleased, if not a little surprised, to see the enthusiasm with which people responded to his post. It was a good sort of surprise, of course - the type of surprise one feels when they receive a gift on their doorstep that they had not been expecting.
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VanderSol prepared to knock on the door. "It's now or never," he said aloud.
The --------- break is always used as a sort of meanwhile... in my story, but the secondary characters never have internal monologue. I went back and took out the main character's inner thoughts to keep it consistent. I suppose I could have added internal monologue to the secondary characters, as well, but I want them to feel secondary, so I have reservations about allowing the reader inside of their heads.
Sounds to me like this is really an issue of different kinds of viewpoints.
You've got normal 3rd person limited for your main character, and you're also doing Objective Omniscient for your secondary characters, and using scene breaks to slip from one viewpoint style to another.
That's not really typical, but I think I've seen something similar in a few Thriller books.
And there are writers who vary viewpoint style quite a bit throughout their books. Stephen King almost always writes in omniscient but he varies the style of Omniscient depending on the type of chapter. Sometimes he's basically doing 3rd person limited with very occasional head-hopping (always used in the correct way so that it doesn't become confusing.) Other times he takes a really distant viewpoint with no access to characters' internal thoughts. There's a chapter in Salem's Lot, for example, where he jumps over the whole town, talking about all the characters and giving an overview of events, and there's a very definite feeling of a disembodied, impersonal narrator.
So, in short, I think what you're talking about can work. The viewpoint character's scenes absolutely can feel a little different than the scenes with your secondary characters, particularly if they are short scenes and only intended as a plot device.
Here's a good site with information on different kinds of viewpoints: http://www.fiction-writers-mentor.com/point-of-view-in-fiction/
My advice would be to read a lot, see how other writers do things, and learn by example. A lot of really good writers break the "rules" very frequently, so you shouldn't necessarily tie yourself in knots trying to follow standard practices. Still, it's good to know what the standard practices are, and why writers tend to do things in certain ways. But what actually works in popular fiction is often very different than what writing manuals will tell you, so when in doubt, always look at what's selling, and what readers enjoy.