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My guess is the majority of Neons out there have dark brown/black brake fluid. It's not unusual at all. You can prolong the life of the seals in the braking system by flushing/changing the brake fluid periodically. If you can get your hands on a power bleeder it makes the job easier. If not, just keep pouring fluid in and bleeding until it comes out clear.
It happens in every vehicle and is completely normal. That being said, I like to flush the lines, and subsequently the reservoir, every pad/shoe change until it runs clear again. Probably about 99% of people never do though.