The only truely supported broswer for SSRS is IE, if you want everything to work as it should do, then you need to use IE.
Remember that SSRS is a MS product and they only test their products with their products. So it is only tested with IE, it doesnt get testing with Chrome, Firefox, Safari etc.
While there is some features that work in one, they dont work in others
http://msdn.microsoft.com/en-us/library/ms156511%28v=sql.90%29.aspx
The only exception to that rule as far as I am aware is Office for Mac.