People are going to come along and ask for pics, since we really can't make judgements about your specific coins without specific pics. But, we can give some generalizations.
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2001-D Rhode Island Quarter: It's got some notable discoloration on both sides.
"Discoloration" is, almost always, environmental damage, rather than some kind of mint error. The coin got buried, or left in a chlorinated pool or fountain.
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2004-P Texas Quarter: I cannot tell whether this is just tarnished or if it's an error.
See above.
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1984 Quarter: There are a few areas where the lettering doesn't seem to have been stamped completely. I'm wondering if it's possible/common for a section of letting to get "rubbed off."
We really need to see this one to make a call, but in general, yes, it's possible for pieces of lettering to be missing from a coin. This might be post-mint damage (something hit the coin, scraping a piece of the letter away), or it might be a "grease-filled die". Chances are it's "just
PMD", but without a pic we can't say; grease-filled dies are common enough for people to find at random. Unless the "missing letters" are particualrly unfortunate or amusing (like the "In God We Rust" coins), they don't attract much if any premium.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis