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Firefox is on the brink of being dropped by the US Government
(www.brycewray.com)
This is a most excellent place for technology news and articles.
It's rarer than is used to be but I know Ive had issues in the past with firefox on some insurance websites, some banking websites, I know Ive seen sites where they block you from even entering but if you change the user agent it works. It's less common than it was 5 years ago though as there is a report website feature and they work hard to try and fix compatibility.
It wasnt firefox's fault though more the web developer. I dont have specific examples because I didnt save them and it's been a while. Its not as bad as during the ie6 days of the internet though. Now that was dark times.
Edit: Also sometimes it's addons and people mistake that for the browser and dont tweak their addons before blaming firefox.