What worries me more is the probability of someone copying over all their basic macros and making the site slow to an absolute crawl for the rest of us.

Another thing also just occurred to me about these definitions. Heading on over to faketestsite, I see that I'm not the only one to think of this: http://faketestsite.stackexchange.com/questions/151/let-me-test-mathjax. To save people the bother of clicking on the link, it appears that \newcommands are global. That means that the \newcommands on one part of the page will affect what happens in another. Since the order matters, and the order can change (it can even be different for different users as some will order the entries by date, some by reputation), this is potentially quite a serious issue.

One thing that wasn't clear to me before was the meaning of MAXMACROS. It's the cap on the maximum number of macros that will be expanded in any given formula. So you might exceed the cap of 50 as follows:

$\newcommand{\Z}{\mathbb Z}
\newcommand{\Zp}{\Z/p\Z}$

Consider the 11-tuple of groups $(\Zp,\Zp,\Zp,\Zp,\Zp,\Zp,\Zp,\Zp,\Zp,\Zp,\Zp)$

Each \Zp results in five macro expansions:
one to convert \Zp in to \Z/p\Z,
two more to convert \Z/p\Z into \mathbb Z/p\mathbb Z, and
two more to conver \mathbb Z/p\mathbb Z into {\bbFont Z}/p{\bbFont Z}

The single formula with 11 instances of \Zp results in 55 macro expansions, so that formula breaks.

MAXMACROS: 10000,    // maximum number of macro substitutions per equation
MAXBUFFER: 5*1024    // maximum size of TeX string to process

Faketestsite is currently running the branch with the fix, but MO is not. I invite you all to go experiment on Faketestsite to see if you can cause trouble of find unexpected behavior.

I've noted at the issue tracker one way to still cause a fair amount of trouble with \newcommand.

(If we could limit the scope of definitions to an answer, for example, we could all start pasting our favorite latex prologue when writing an answer... :) )

What is the scope of a definition? The whole html page?

I think it's everything on the page below where the definition is made.