Design away, my friend. The Apple display packs many pixels.
A window will open to fullscreen on the Mac, no problem. It simply conserves space when it can, unlike the PC behavior, which will fill the screen regardless of how much space the site actually needs.
In other words, the case where the Mac doesn't open the window fullscreen is the case where the user has room to spare. So those are cases you don't need to worry about. If a Mac OS browser has to go fullscreen to fit the site, it will. But when the site is only 960px and the user has a gorgeous 2560x1600 cinema display, it will stop at 960, enough to eliminate the horizontal scrollbars.
The reason people notice this behavior is because apple displays are often too big, so the fullscreen is often not needed. The smallest display Apple ships on any notebook is a roomy 1280x800. The smallest iMac is already 1680x1050. They only get bigger from there.
As far as choosing your dimensions, the normal considerations apply. Play to your lowest common denominator. Simply know that the screen resolution of even a modest apple display will be on par with the industry standard. If you're willing to go 990 or 960 for the PC, it will also be acceptable for the Mac.

(source: akamai.net)
Most of the designers I work with are more concerned with making designs too narrow for Apple users. They design in the 960 pixel realm so that it works for the larger audience, and then they try to find creative ways of showing a little extra love to the owners of that giant cinema display.
Sidenote: @Taylor Marshall asks a good question: "What if the widths are all set to 100%? How big does [the browser window] get..?"
Without any constraints, Firefox will simply go fullscreen, like the MS Windows behavior. Safari will expand up to a width of 800px, unless the width is already greater than 800, in which case it maintains that width and only modifies the window height. Of course, if there aren't any hard width values, then the design is a liquid layout, so the concern about designing for a particular width is somewhat altered. Usually good liquid layouts, despite being displayed correctly at any dimension, are nonetheless designed to be viewed at reasonable window widths.