In particular, It looks strange to me than the 'TeX' path is repeated in the URL. If I type the same URL without the duplicate 'TeX' in my browser, it works.
I also tried with a local copy and ran the test application of MathJax (which was OK), fixed the paths, this looked better but still didn't work.
Older versions of this plugin had the TinyMCE release number hardcoded. Moodle releases 2.5.6, 2.6.3 and 2.7 are now using TinyMCE 3.5.10. The current version of Mathslate plugin here now checks for correct release, but you need to upgrade. Older versions will fail to load.
MathJax now requires loading of an extension for using jax.root.toMathML. The TeX tool in Mathslate uses this. The MathJax documentation has a warning to implement this usage as a callback rather than synchronous to avoid loading errors.
Moodle 2.5 and 2.6 contains a standard theme Formal White which uses fixed widths for the left and right columns of 200px in popup windows. With the default Mathslate window of 400px there is not enough roome left for Mathslate to be displayed even though it loads successfully. The result is that the window displayed is completly white. Mathslate is revealled only when the width of the image is enlarged.