I signed up here for a few reasons and researching this issue was one of them. Thank you for the thread!
I have Cute Editor running on a few websites as well (and other than this and some minor issues we really love it!). This changing of Flash embedding code causes major problems with just about every browser except IE on my PC. Everything looks fine, but when I switch to Firefox, IE/Mac, Safari, etc. there is nothing on the page's frontend except blank white space. Taking a look at the code and doing some reasearch I found that it was indeed that Cute Editor was changing my code around, and clicking 'HTML' and trying to change it does not help as it just changed the code back once I save the changes.
Disabling the AutoFormatting might be work well, except I am pretty happy with the formatting other than this.
Other than that, and some minor issues, Cute Editor has been a huge help on our projects.