You've probably made an error in your HTML. Check using the Mozilla validator extension.
Do not assume it's a bug in Mozilla because your code doesn't work in it.
I notice you haven't given the frame a name, this will mean that you can't target links to it with anchors. The popup blocker will assume that these are popups (as a frame with a name which doesn't exist will popup a new window) and block them. This is its designed behaviour and not a bug.
MSIE probably does something else, but it has very little adherence to any web standards, it just does its own thing, by and large.
Another thing to look at carefully is how you escape the model code for the query string. No matter what MSIE may think, URLs containing spaces are NOT valid.
Mark