When you add a media item like a video to the page, it is really the wysiwyg editor that creates the markup for embedding the video. So if it is a bug it would be a bug in the editor.
The editors we use are open source editors (CKeditor and TinyMCE), so if we find a bug we have to report it upstream to the editor project.
When we do upgrades for the editors CKeditor and TinyMCE, we version the folder like /ClientScript/ckeditor36/
and the version used is configured in Web.config so if you upgraded the old version of the editor is still on disk and you could switch back to it from Web.config if you need to.
But first I would verify it by compare the markup for an existing video which works in IE to the markup of a new video that does not. If you find that the format of the embedding code is changed or wrong then it probably is a bug in the newer version of the editor and switching back may solve it.
You could also try a different editor and see if one works better than the other. From Administration > Site Settings you can choose CKeditor (the default) or TinyMCE.
Hope that helps,
Joe