Thanks all for the replies.
Here's an update on my situation. I went to the shop that sold me the dirt and they were surprised and weirded out. They had no idea what it was but suggested that I call the manufacturer. I called the manufacturer and spoke with one of the co-owners. She was very pleasant and I e-mailed her a link to the photos. She is going to investigate and see what she finds out from her end.
I then took a bunch of the worms to our local vet's office/animal hospital (small animals - mostly cats and dogs). The staff was very freaked out by the worms and they got their vets (their were 3 vets present) to look at the worms.
The vets said that they had never seen this particular worm before. They said it does not look like a round worm that is common for a cat or a dog, but one vet said it does look like some kind of nematode (round worm). They didn't know whether or not it was parasitic but suggested that I take it to the University of New Hampshire's cooperative extension to have them look at it.
Before I went to the vet's I called the Univ of NH Coop. Extension and they said to bring it in. They normally identify bugs, but the person I spoke with said they would look at the worm as well.
My concern is that the worm might be parasitic - some kind of intestinal parasite. I only noticed the worm in the garden that I spread my extra bag of Moo Grow Potting Soil. Curiously enough, I put two bags of Moo Grow into two 16" pots yesterday as well and did not see any worms there.
I wonder if the rain and the composte might have drawn the worms to the surface. Anyway, the worms are pretty creepy and I'll post some additional pics.
It was funny - everyone that I showed the worms to were completely weirded out by it. At the garden store, the staff was all amazed at it and one customer who saw them was very excited and anxious. He was totally shocked by the worms.
At the vet's office, the staff was really freaked out by the movement of the worms (they twirl around and move A LOT - that's why my eye was drawn to them in the soil, even though I was standing about 6 to 8 feet away). We used a pen to move the worms so they could see them better and afterwards the staff promptly threw the pen out in the garbage they were so weirded out! They gave me a glass test tube with a rubber stopper to store some of the worms so I could give them to the university. They were very helpful, even if the vets did not know precisely what it was.
Anyway, here are some more pics of the worms. Yes, they do look like roots or fine pasta.
Here's a low res pic of the worms in a test tube. Note that in the photo they are curled - that's because they are writhing around in the tube. it was tough getting the worms into the tube. I used some tweezers that the vet staff gave me and the worms coiled around the tweezers and around the mouth of the test tube. I told the staff that it reminded me of the movie Slither and one of the staff members, who saw the movie, agreed.
Also, here's a link to a larger resolution version of the picture,
I'll post an update when I get more info.