Well, the bold part is not true. hosts purpose is different and using it to block (most often by redirecting to localhost, actually) is just a clever trick. So, can this be change to "which can be used to block access to defined sites"?
Also, lots of information in this FAQ also will be useful to users having problems with update and comment forms, as well as other parts of site that use scripting, so can it be made more general to apply to such cases as well?
In that case, following information may fit this FAQ well (after editng it to fit to FAQ style, of course, since it is gathered from answers on support board):
* Possible source of problem could be security settings in your browser. Most browsers allow to set different security levels for different sites. You may want to lower security level for livejournal.com or add it to trusted sites list to allow LiveJournal's scripts to work properly. (already mentioned as possible source of problem with stat.livejournal.com, but also applies to scripting).
* Other programs, such as anti-virus software, pop-up blockers or software firewalls may also prevent scripts from functioning correctly (already mentioned as possible source of problem with stat.livejournal.com, but also applies to scripting).