A few interesting things I learned:
1. Knuth volume 2 has an extensive discussion of the problem space. I've only gotten a chance to skim it so far, but it looks interesting and approachable.
2. I need to support bitwise operations, which operate on a two's complement representation, so I figured it would be simpler to use two's complement internally, despite seeing that most (all?) bignum libraries use signed magnitude. I'm starting to regret this: two's complement introduces a lot of complexity.
The most fun thing about working on a bignum library is that it makes the algorithms you learned in grade school for add/subtract/multiply/divide relevant again. The basic ("classical") algorithms on bignum are basically exactly the same thing you learned in grade school, except on a much larger base than base-10.