We harvested all of the remaining carrots in our garden, and to our surprise a large number of them are white or bright yellow in the center, rather than being orange all the way through. The white carrots taste fine (very sweet and crunchy), but they don't look like any other carrots that I've seen before... more like a carrot that swallowed a parsnip. What causes this? Is it a problem?
It's perfectly normal. All carrots have a core, sometimes they are different color than the outside of the carrot. (I planted red carrots with an orange core last year.) The size of the core depends on the carrot variety (e.g. Nantes coreless has -- surprise -- a minimal core). Varieties with wide shoulders will have a bigger core. You can also end up with a bigger, tougher core if they remain in the ground for too long.
If the appearance of the white core bothers you, try planting one of the "coreless" varieties next year, and be sure to harvest before they get overmature.