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Firefox good! Flash with Firefox bad! (think... bad frankenstein accent)
This is a common problem with many plugins in that they inhabit a layer (or z-index) that is outside of the main document. Which means that layers and drop down menus will be seen to be hidden 'behind' the plugin object.
There is no easy solution to this that I know of I'm afraid. It is similar to IE select elements appearing 'through' layers that are above them. The only solution I've seen for this is to toggle the display property of the select element to none (or hidden) when the layer is over them!
HTH