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limbo - 9:49 am on Nov 23, 2012 (gmt 0)
Responsive Layouts are not going to sort browser bugs. Validating your CSS/HTML and using a reset will.
Responsive / mobile first design, will however, enable your site to work on a variety of screen sizes an resolutions - but takes a lot more work (like another 50% on top of the design/front-end budget).