More pics

Here is another pic

I know ive personally had my battles with chatter in the past and doing some research it turns out theres numerous reasons why chatter occurs.

Thats pretty bad. Thats almost a mixture of chatter with some dishout too. That wouldnt fly in my eyes. Some light chatter you might have to live with. Dince subfloor issues is a primary cause of chatter its tough to say whether or not you have that issue. But im more concerned about the dishout.

I would discuss it with him about your options. Keep in mind though that theres not much he can do without resanding

Yeah I'm a little bummed. They also missed sanding some spots that had paint splatter from the previous owner, which now have paint splatter under finish, missed spots with final finish coat, burned through brand new vinyl tile in 2 locations, had urethane drops that dried into quarter-sized pools in several locations, and left huge round-sander marks on a transition between the wood + tile areas.

I've paid them for half the job up front, but am not sure I want to give them another go at a sand and refinish. What would you suggest as a good compromise?

Personally I find the other issues you mentioned to be worse than the chatter. With widespread use of Trio type machines, standards have risen although they can be influenced by what you're paying. The more you pay, the higher standard you should expect. Why? Because essentially you're paying for a cosmetic issue that has little or nothing to do with durability or usability. A floor that's 95% perfect won't last any longer than a floor that's 85% perfect but it does take more and more work the closer you get toward perfection. Another consideration with chatter is that once you put in rugs, furniture and window treatments the chatter will be much less visible and it doesn't affect the usability of the floor.
However, coupled with the other issues, it's pretty clear that the floor will need to be resanded. Before resanding your contractor should inspect his machines. Your waves look more like dish out which is caused by too much drum tension, walking too slow or walking at an uneven pace. Chatter is generally more uniform and can be caused by several things.
http://hardwoodfloorsmag.com/articles/article.aspx?articleid=46&zoneid=1

RE: "Well thats tough. Is this just some joe blow guy off craigslist or a professional company?
I think either way you kinda need to give him the opportunity to resolve these issues.

Point out Everything to him.
If hes a true professional he'll fix everything and make things right."

It's a pro business with good references. I think this one may have been subbed out though :(

I had another reputable company come in to take a look last night and they too thought it was a pretty bad job. He spotted a lot of dishout, some chatter, oil splatter, no filler used, areas with finish missing, etc. Turns out I'm not crazy at least. His thought was that the equipment needs calibration. Although the other business was willing to attempt a fix, they too thought it would be best to first talk it through with the original installer (and I agree).

I'm definitely going to talk it through with the original installer first--- the owner seemed like a good guy from the get-go and I bet he'll want to make it right. I just wanted some second opinions before I talk business.

It's a bummer either way because it puts a serious hold up in a series of renovations I am working on. And, although I thought I was getting a new floor, even if he sands it flat my new floors are already that much thinner from the re-sand.

Trio-type machines was mentioned in this thread. I have been using the Trio in my work and I never wind up with chatter or any other visual sanding error in the final result. The Trio not only corrects small issues left by the belt machine and the edger...it reveals errors that a machine operator might not see prior to applying a finish material.

Hire someone who uses a Trio-type machine in the work and you probably will get close to a flawless result.