*Access data for all web sites
NoScript needs to inject content scripts inside each page to create placeholder for replaced elements. Once a script run inside a page, can access all its data.
*Read and modify privacy settings
NoScript needs it to tighten them.
*Access browser tabs
Same as above, in order to decide what to block it needs to know which site is navigated.
*Store unlimited amounts of client-side data
Whitelists / blacklists can grow considerably...
*Access browser activity during navigation
This is for webRequest, the main API allowing NoScript to analyze load attempts and block the unwanted ones.
Sorry for the silly question, I can see why it would need access to these things butI've never seen them with a firefox installation before (guess it's the new system) and it's worded a bit ominous.
Still, if it was a Youtube skin or some flowered theme claiming to need those permissions, I'd like to know in advance