Is it possible to fix this bug without downloading an older verson of it?
When I click on the search text field on top right side, it keeps on blinking.
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No, to fix a bug you just need the buggy version installed. Then go to the Firebug plugin directory and fix the bug directly in the source.
If you do not want to do this check if your bug has already been reported in their bugtracker, if not report it there and wait for a fixed release.