Don't remove the cover, as it protects the bulb. Removing the cover will allow water and dirt to contact the bulb, causing it to burn out VERY quickly. See the good answers below for possible cures.
Get some light buffing compound and buff the oxidization off the lens. This might take a few applications and wont take 100%of it off.
As mentioned before, a good rubbing compound can help clean it up. Meguiar's has a good 2 step system with 1) clear plastic cleaner (#17) and 2) clear plastic polish (#10) which are available at most auto parts stores. I have spoken with several body shop guys, and they've told me that after polishing, try taking some "clear coat" spray on touch up paint (has to be a spray) and put it on the headlight cover. Just be sure cover everything you don't want painted around the light. Doing this will help preserve the polishing you did. If it is not clear coat painted, count on having to re-polish about every month or so. This clouding occurs when the factory clear coating on the light deteriorates. Ford seems to have the worst coating over the plastic lenses of any manufacturer that I have ever seen.
The other option that you have is replacing the headlight assembly (this will cost some money). This will give you a brand new factory clear coat that will probably start to go bad in a year (two years at most).