What about if you declare a "type" for your link? Also, you can try a rel of simply "icon" in addition.
Try this:
<link rel="icon" href="/images/favicon_muse_me.ico" type="image/x-icon" />
<link rel="shortcut icon" href="/images/favicon_muse_me.ico" type="image/x-icon" />
You could also try appending the domain to the image src as well:
<link rel="icon" href="http://www.musememobile.com/images/favicon_muse_me.ico" type="image/x-icon" />
<link rel="shortcut icon" href="http://www.musememobile.com/images/favicon_muse_me.ico" type="image/x-icon" />
UPDATE
You could also try using a png for your favicon (obviously will need to have a png version to do this). This is the approach I take with my own site and it looks fine in Chrome:
<link rel="icon" type="image/png" href="/images/favicon_muse_me.png" />