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I am seeing something funny and maybe I'm misunderstanding how the CSS compression works, but I didn't find anything about this in your documents concerning the Adaptive Theme file generation system. You can observe this effect at http://store.bevelsmith.com/
Inspect the page using firebug, in particular the views slideshow
If I turn off CSS aggregation/compression (see http://stage-store.bevelsmith.com/ - I've turned css compression off on my staging site) you can inspect the same element and see that the path is correct - url("../images/slideshow-shadow.png") no-repeat scroll center bottom transparent; - so the image is displaying as desired.
Have you seen anything like this, or do you have any idea where this errant file path is coming from? Full disclosure here - the store.bevelsmith.com site is a multisite installation, where store.bevelsmith.com is the main site, and I create multisite installs using this as the base site. That said, there is no multisite install called udmg81 so I don't know if this is contributing.