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To expand on the problem (i think) that Smithcraft is mentioning. OS X tries to be smart when you launch an app that's close to an edge of the screen. So if you launch OmniWeb and the window is close to the right side of the screen, the tab drawer will automatically open on the left for that window.

The solution here would be to move your window further to left and then "Save Window Size" (via the Window menu).