I have been digging up carrots and have lots left in the ground. All of them are soft and spongy right out of the ground. I have been eating them for three weeks or so. They seem to be safe to eat. Did I just over-water them? Are they really safe to eat?
Soft and spongy might actually be a symptom of carrots that are low on water. Water within plant cells provides pressure to support the cell walls. As cells lose water, this support weakens, and can cause cell walls to sag. This can give the "soft and spongy" sort of texture you describe when you eat it. Carrots can re-hydrate somewhat if placed in water for awhile, so you might try submerging a carrot for a couple of hours to see if that produces a firmer carrot. Not knowing more details, it could well be some other cause, but I observed this behavior with some carrots that had been in the ground for awhile without getting any water.
I don't know a lot about carrots, but I'm guessing they need more potassium (if you're deficient in calcium or silica that may also be an issue). Those three things really strengthen stems of plants: I imagine they do similar things to roots. If you like soft carrots, I wouldn't worry about it much, though. Potassium and phosphorus are said to play a role in root development, too.
Potassium will likely cause your carrots to absorb more water, too.