I suspect that MoinMoin's wiki markup language is interpreting some of
the mathematics as its own markup, and converting it to HTML before
sending the page to the browser, and then MathJax won't recognize it
as mathematics (since math can't contain HTML). For example, I
suspect that the ^ symbols in the third example means something to
MoinMoin, and it is replacing "^2}{K^" by something like "<sup>2}{K</
sup>" or something like that. You may have to use special escape
characters (like backslash) to prevent MoinMoin from interpreting the
^ as its own markup. Alternatively, you may be able to force
"verbatim" mode in some way so that it leaves your characters
unchanged within the mathematics. If there is a way to get MoinMoin
to produce a <code> block, for example, that might work, but you might
also need to change the MathJax configuration to allow MathJax to
process the contents of code blocks. (You would have to remove "code"
from the skipTags array in the tex2jax block of your configuration;
see
http://www.mathjax.org/docs/2.0/options/tex2jax.html for the
default value of the skipTags array.)
Davide