In my opinion, it is sensible that 0 and $0$ are typeset differently. I think they have different purposes. Not all numbers are mathematical numbers.
For instance, when I say see Section 1, the 1 is a piece of text, not a piece of maths. Another example: a phone number - again, that's text, not maths.
Often it doesn't matter whether you type 0 or $0$, since LaTeX tends to use Computer Modern both for text and for maths. But when this default is not used, the text/maths distinction becomes visible in the output. For instance, I like to put \renewcommand\rmdefault{bch} in the preamble of my documents, to change the text font to Charter and leave maths in Computer Modern. Or maybe you're making slides, and want all the mathematical text to be highlighted in green.
Here are a few examples of the text/maths distinction in practice.
\documentclass{article}
\renewcommand\rmdefault{bch}
\begin{document}
In Section 2.4 we learnt that $2+2=4$.
\end{document}

\documentclass{beamer}
\usepackage{xcolor}
\setbeamercolor{math text}{fg=green!60!black}
\begin{document}
\begin{frame}
The maths hotline on 0800 123 123 told me that $2+2=4$.
\end{frame}
\end{document}

theoremenvironment. – Display Name Jan 03 '11 at 03:24