Oh, all the time. Hannity routinely takes comments out of context to ascribe statements to people that the opposite of what they actually said. Obama had a speech where he said something to the effect of, "Some people say we're in decline. I disagree." Hannity quoted and ranted, "He said, '...we're in decline'! he hatez america!" They've edited video to distort the plain meaning of what someone was saying. And wasn't it them who touched up photos to make two journalists, who were reporting something embarassing to the Republican Party, look 'more Jewish' ? Why yes, Mr. Orwell, it was.
Seriously, there's a conservative case to be made on most issues, but Fox news will not present it or anything else but the most brazen political propaganda. Other media outlets might get the story wrong, might emphasize something irrelevant (though usually in a rightward lean), but Fox is a party organ in the style of Pravda.