I have been having trouble with the WMODE="transparent" embed setting in combination with Firefox. What I wanted to do was show a SWF on top of some HTML with the background set to transparent. Turns out that it’s just not possible in Firefox.
One issue was that the user had to click into the SWF at least once for the dragging functionality to work properly. Otherwise an item would lag behind the mouse.
The biggest issue I had was that the keyboard input would somehow get "reset" to the English layout. This means that anybody using a non-English keyboard would get strange results while typing. This keyboard bug has been known since at least 2005.
In the end I just loaded a dummy image into the background of the SWF instead of making it transparent. All the other browsers behaved fairly well with the WMODE setting.
If anybody else is having these issues, head over to bugzilla and vote for getting the bugs fixed.
In conclusion, consider WMODE="transparent" a last resort for even the simplest Flash projects.