A new version of SwfObj just shipped out of the factory today. This release fixes a couple of bugs that were recently brought to my attention by users like you.
Taming the big bully
Apparently, unknown to me, this plugin has been inserting swfobj shortcode whenever a media object is imported into a post from the Media Library, whether it is a Flash object or not. That kind of over-aggressive attitude is not welcome around here. As a result I added a media check to the import function. Now the swfobj shortcode is only inserted when embedding Flash objects. I also sent the plugin to time-out and told him he needed to apologize to everyone for his bad behavior.
A minor bug fix that most people probably won't notice involved cleaning up the class attribute. It was being added to both object tags as well as being placed in a defunct param tag. The class attribute is now only applied to the outer object tag and no defunct param tags to speak of.
I'd also like to take this chance to thank all of you who have sent in feedback both good and bad on this plugin. Thank you for taking the time to contact me so I can continue to improve the SwfObj plugin. And a very big thanks to the generous person who recently sent me a donation as well!
Please continue to send any bug or feature requests you have. All feedback good and bad is appreciated.