Earlier quoted context omitted.
In the Firefox preferences go to the Privacy tab and select Use Custom Setting for History in the History section. From there you will see the check box to accept 3rd party cookies. Keep in mind this will prevent webmasters from using things like Google Analytics. Which you may want anyway but I thought it was worth mentioning.
Are you sure that setting "Accept cookies" to "off" will prevent third-party sites from reading cookies as well?
So if you go to facebook.com and it sets some cookies and later you go to somerandomblog.com that has some images from facebook.com, Firefox will not send cookies to facebook.com, since you are not visiting it directly.
Now obviously if somerandomblog.com has javascript from facebook.com on it, then that javascript can read cookies from somerandomblog.com and do pretty much anything it wants with that page.