Criticizing other people's figures on my webpage
I can't even imagine a situation in which criticizing published academic materials on their merits would be wrong or immoral.  

How would it be different from criticizing someone's selection of an econometric or statistical model to use on their data?  This happens constantly in academic literature, and in fact is crucial to the process of research.  The way data is conveyed to others through graphs is no less important than model selection, and both can be used to deceive or obscure.

So as long as you cover two bases:


Avoid ad hominem attacks, as you should in all sorts of reviewing, and
Follow any copyright rules the publishers impose,


Not only is there nothing wrong with doing it, I would argue that as an academic and data viz expert, you should do it.  As for someone taking offense at your criticism?  Well, as long as you're professionally criticizing its merits and avoiding problem number 1 from above then it's you who are in the right, and the one taking offense who is in the wrong.