I just noticed that Stack Overflow employs Firefox only CSS to round the corners of the user badges on the front page. It’s an interesting idea but what would be the pitfalls and advantages of using Firefox only CSS (aside from the blatantly obvious ones)?
-moz-border-radius:6px; -webkit-border-radius:6px;
Above: The CSS used to round corners on the Stack Overflow front page.
The main problem would be, as I see it, that your css wouldn’t validate. Other than that I see no reason why not to use this type of platform specific features as they don’t cause any harm to users whose browsers don’t support the features.