Wow, Olegis, that's a great image at ISO 800! Unprocessed, it's quite sharp. I don't think I can quite give it the "tack-sharp" seal of approval, but it's definitely very close and it is very sharp. After a little PS sharpening, that does look awesome! Is there anyone out there with the Canon 24-70L that would like to comment on that quality at ISO 800?
OK, after seeing Olegis' image at ISO 800, I did a little playing around, and I think I've found the crux of the issue. In those dark indoor conditions, even at ISO 800, I'm still underexposed by about 2 full stops (at this last event I shot at f/2.8 1/320 sec ISO 800). That's making the image look grainier, and also, unlike the cat, which is a single giant object that fills the frame, I'm shooting a group of people, so the grain on any particular subject's face is going to be more noticable because the subject is so small in the frame. Is this correct reasoning? Anyhow, I just took some shots in my home at f/2.8 ISO 800, but properly exposed, and the image looked much closer to what Olegis posted. So, it looks like if I had the Tamron lens, I would get similar results to what I get now, except that I would have that cool zoom capability. Thanks again Olegis for the sample. BTW, do you have any samples at ISO 800 that are about 2 stops underexposed? If so, are they fairly grainy? 
Tim, thanks for the offer, but I think I've seen enough. I'll save you the trouble, and I do appreciate the offer. 
I've considered selling the 1.8 and buying a 1.4, but that's a lot lower on my list right now. For now, the money is going to be better spent (for me) elsewhere. But it is a definite thought. I am noticing that I'm getting a few shots off focus. Now most of those are probably me, but quicker (and more accurate) focusing would be nice. At the time, I just couldn't resist the $80 price tag of the 1.8.
My focusing technique is to use AF in One Shot mode using the center dot as my focus point. I try to focus my subject, then keep it held, and shoot when the moment presents itself. I shoot in continuous mode so that I can get a jump sequence or whatever and choose the best shot. Everything's happing so fast, I just have to shoot a lot and hope for the best! Most shots are in focus, though, especially since I'm now up to f/2.8. I was using f/1.8 and that was brutal because the DOF was so narrow.
Ron, you are right, if the 28-105/2.8 was any good, not only would people be talking about it, they'd probably own it!
Yeah, it really did look almost too good to be true.
As for prime lenses, the input from this forum turned me onto the 50/1.8 and I have been so happy with it! One of the lenses I want to get after this 24-70 or 28-75 (the 28-105 is now out) is the Canon 100mm macro lens (macro shots are cool). This lens opens up to f/2.8, so I could use this lens at events as well. I know that the Canon 100 f/2.0 would probably be better in this situation, and it would be better for portraits as well, but it would be nice to get multi-use function out of the lens. Anyhow, it's all something for me to keep in mind.
Thanks for all of your input. I think I'm leaning (heavily) towards the Tamron 28-75XR Di at this point. $340 vs $1100 is a huge difference. At that price, I probably wouldn't even be upset if I ended up buying the 24-70L a few years down the line. Then again, maybe I would. But, that would give me the $470 I would need for the Canon 100/2.8 macro. Or $375 for the 100/2.0. Or $325 for the 85/1.8. What if money grew on trees? 
Thanks again for the help. I think I need to just let this all settle in the back of my brain for a little while.
OT: BTW, I have email notification set, but it's not working. Is it working for anyone else? Thanks.
-Deva