Bicycle Mechanics - Wobbly Sprocket

I couldn't find anything specific to my problem. I was trying to adjust my rear deraileur and I noticed that when my wheel spins, and the chain is idle, the sprocket wobbles a little bit. I don't do a lot of repair on bikes, so I checked out my other bike and it doesn't do it on that one. Should I be worried. I'll try to explain what parts I have. It's a Trek 1000, and I'm not sure about the wheel or sprocket. I took pictures.
http://farm4.static.flickr.com/3280/2457338775_5f58de0321.jpg?v=0
http://farm3.static.flickr.com/2012/2457338961_cb94c57468.jpg?v=0

So, when I have to bike upside down, I get the wheel going by cranking the pedals around. The sprocket seems to rotate every so slightly around the quick release pin that goes through the wheel (sorry I don't know what they're really called.) Also, the bike bounces a little bit, especially when you really get the wheel moving fast. I hope this is detailed enough. If there's anything missing that will help diagnose, I'll be glad to add. When I get a better camera (left it at work) I can make a video perhaps.

Thanks in advance for any wisdom. :D

After I posted this, I thought I might want to take out the quick release pin and inspect it. It appears to be bent slightly on the side the sprocket is one. Does this affect the spinning of the sprocket? I could see why and why not, I just don't know for sure.... :/

This was mentioned in another thread. You do not say what brand and quality level the hub, freehub and cassette are. I can tell you that in brand new bikes with low end components this is a very common thing. Most never notice it and it does not appear to have an adverse impact on shifting or life span. I know exactly what you are talking about having noticed it at the shop where I work part time.

Explanation: Lower end components have more lax tolerances. Put a low end freehub / hub with a low end cassett and you will see things like the cassette appearing to wobble (it actually is).

Most people never notice it and it should not impact your shifting.

If your components are say Shimano 105 I would not expect you to see that and would look at freehub and/or cassette wear. It would be unlikely that the skewer would cause it.

I saw a low end aluminum freehub last night where the steel in the cassette had eatin into the ridges. That can eventually lead to not being able to remove the cassette at all. Again, low end components.

Yeah, they are definitely low end. I replaced the wheels and sprocket about a year ago, as cheap as I could get them. It's just my grocery bike. I wouldn't have noticed it had I not been working on the derailleur. Thanks for the input! :D

I was helping my friend with some bike maintenance tonight and noticed the same thing. I was afraid he had a bent axle:(
Thanks for the input, F. Thomas!