k, I've gotten a chance to look at this a lot more now. To clarify, I do have two entire trackball setups. I tried both trackballs on the problematic machine. Both perform the same, and the controls are weird and over sensitive.
Then I tried both trackball assemblies on my other arcade machine. Both trackballs worked just fine! They are not over sensitive, so the slight drift (which we've all agreed is normal to some extent of every trackball) does not affect the gameplay. So that means this is not a hardware thing any more. This is a software problem.
What's weird about this, is that when I started the second arcade, I copied over the entire MAME folder from one machine to the other. So we should be working with the exact same software here, as far as MAME goes. Now, just in case, I recopied over the MAME folder from the working machine back over to the problematic machine. This did not fix anything. The trackball is still weird and over sensitive.
Now what I did next was go into the control panel, and compare the settings on both machines. They both look exactly the same, like this:

(Now I know I did not yet disable hardware acceleration yet, more on that later).
So anyway, those settings on that tab appear to match on both machines.
Then next I checked out the driver for the mouse being used on both machines. Both appear to be using the same driver, same version, as shown below:

The lastly, I compared the registry settings from the working machine to the not working one. I changed them so they matched the working machines settings. Those settings are shown below:

After updating these settings I rebooted the computer and tried again. The trackball still acts weird.
So I can't really figure it out. From what I've described above, it seems like the same settings exist on both machines, however the same trackball acts different on both machines. So I'm not sure what to do.
I thought it was weird that the trackball worked on the other machine, despite the mouse acceleration stuff still being enabled. I'm not going to touch the working machines settings. Whatever it is they're doing, it's working. But what I tried to do next was disable the mouse acceleration on the non-working machine. I did this using the direction from the link I posted earlier:
http://kaioa.com/node/68This actually didn't do much good either.
Also tried this to no avail:
http://www.tweakxp.com/article36785.aspxSo now I'm back at square one. I at least figured out that it's likely a software thing, but I'm not sure what else to try now.
The only other thing I can think of is that I have a more regular version of Windows XP on the working machine. On the not working machine, I have TinyXP installed on there. But I wouldn't think that should make any difference.
Any ideas for me?