I am planning on using this technique in building my first puppet. I have already purchased some of the supplies. Thanks for the tip!

Yeah, there are problems with this one, just like with any armature. From what Marc_H said, I would try using nylon washers (or multiple washers between the eye screws). I haven't tried this yet - nor the idea of doubling up eye screws. I think the latter is a bit more inconvenient, since the dowel isn't that thick and cracks easily (you would need something to hold it steady and probably a drill to make nicer holes in it).

As for gluing the eye screws into the dowels - here is my tip: The most important eye screw to glue into a dowel is on the foot - this is cause when you make him walk - the screw might try to rotate under the armature's weight. DON'T glue the eye screws into the dowel where a multi-planar joint is required. This is pretty much the shoulder (both forward and backward as well as outwards) and the hips to leg connection. If you are confused move your own body and see which joints move in multiple directions. (For example, the elbow only closes and opens in one direction).

Hope this helps - good luck next time.

Well, that depends. I designed the puppet more for clothing/ foam use. I don't know how it would hold up with clay around it, but sewing clothing and adding a little foam (for fattening) here or there should work well. Be warned with clay: 1) it would be heavy, 2) you wont be able to easily readjust the bolts in-between scenes, and 3) you'll wanna place some thin plastic between the joints and the clay so as not to get clay stuck in them.

Here is the video of it in testing action - I tried to force it into an extreme position to demonstrate its stability: http://www.youtube.com/watch?v=DDJdFArdH4Y

JesseOffy, that is such a good idea for armatures. I actually work at a hard ware store, and have been racking my brain for months trying to come up with something simple yet effective. Thankfully I looked in the forums (something I rarely do sadly). I built one joint today to see how it would work, and as others have said, the nut tends to unscrew as you move the joint. So I fiddled around until I came up with this combo: I used a screw post, two eye screws, one o-ring, and some red thread lock. Worked like a charm. I was agitating the joint all day, and it never loosened up.
Sadly I forgot it at work, so I don't have a picture of it, but I did create a pic showing what I did:

yeah they make the screw post small enough. ill try to post a picture on thursday. You put the red thread lock on the screws threads, then tighten it down as tight as you want the joint to be. let it sit for a couple minutes, and then the joint is basically glued for life (with red thread lock you have to heat the treated part with a torch to get it apart). here is the brand I used:
Permatex High Strength Threadlocker

If its to tight and the thread lock is already set, you can make it move a little bit easier by applying a small amount of silicone grease on the joint.

edit: when i mean the joint is glued for life, i mean the screw post, so you don't have to worry about it coming loose