That are features that initially only worked in mozilla and webkit based browsers. IE9 supports them also. IE8 most likely doesn't. So you shouldn't use them if you want people with IE8 to enjoy the full beauty of your site.
More on one of them (just as an example): http://www.css3.info/preview/rounded-border/
I doubt if it explains all the issues with your site in IE8, but certainly some. So maybe it's time to go back to the drawing board.