I've also noticed this problem and found that when (using JSAPI 1.4) esri.js injects the stylesheets into the <head>, it tries to inject two links to stylesheets as well as all of the JavaScript references. These stylesheet references show up in IE8 debugger as:
<link href="[object]" rel="stylesheet" type="text/css" media="all"/>
<link href="[object]" rel="stylesheet" type="text/css" media="all"/>
When I look at the same page in FF3.6, the same lines in the <head> look like:
<link rel="stylesheet" type="text/css" media="all" href="http://esri:8399/arcgis_js_api/library/1.4/arcgis/css/jsapi.css"/>
<link rel="stylesheet" type="text/css" media="all" href="http://esri:8399/arcgis_js_api/library/1.4/arcgis/js/esri/dijit/css/InfoWindow.css"/>
So for some reason, the library can figure out how to determine the URL when processed through FF but not IE8 (without compatibility mode). I don't know enough about why dojo is determining the URL correctly in one browser but not the other to fix this myself.