This isn’t a WordPress issue.
An RSS feed is an XML document created by your server for end users to consume updates or changes through an RSS reader. A web browser is not an RSS reader.
Every browser will handle an RSS feed differently – and they’ll do even stranger things if they don’t recognize it as XML.
Often, Chrome will see the feed and render it as a regular XML document – Chrome includes special parsers that clean up and format the display of an XML document to make it easier to read.
Firefox and Safari both see the feed and recognize that it’s an RSS feed. Each of these browsers actually has a mini feed reader built in, so they’ll try to parse the feed as a feed and will display it very differently than Chrome.
If you see errors, it’s likely a problem with the markup or encoding that prevents the browser from recognizing the file right away. If you want to really test your feed, use an actual reader (i.e. Google Reader).