Potential cross-browser issues with layering on top of flash?

I layered an html menu on top of flash in one of my previous projects, and it did weird stuff on Safari (the menu would blink and the cursor kept disappearing.)

For my next project I want to have a flash background which will fade to different colors depending on what site its currently on. I’ll be layering my webpage on top of the flash using CSS2. Will there be any cross-browser issues with this?