Does the Burn Notice premise make any sense?

As VoluntaryPlan noted, the intro is a left-over from season 1, where he was being tracked by the government after he was Burned.

Even if he’s not being monitored anymore, he still wants his old job back, working for the USA. He can’t do anything that would annoy them, like working for another country; that would make him hard to find, like moving around under false aliases; or go against their rules, like that he stay in Miami.

Well, at this point, he might not care about his old job. He does some pretty fun work now, anyway, saving the day and rescuing people and stopping bad guys. If he did just leave, well - where would he go? Why would he want to be there? He’s aparently something of a closet patriot - he’s not going to work against the States, so defection is out. That leaves criminal use of his skillsets or being a freelance avenger - which is basically what he usually pretends to be and actually is right now (respectively).

He still wants his job back, quite definitely. It’s pretty much the only thing keeping him from marrying Fiona. That any time he could get his old job back and be an international man of mystery, too busy to settle down, is precisely what he keeps telling her to turn her down.

[spoiler]Small nitpick (Maybe I should change my title to Picker of Small Nits. :D): This was still season 3. It was split in two parts. Part one began in June 2009, and part two started airing in January. Season 4 begins in June 2010.

http://en.wikipedia.org/wiki/List_of_Burn_Notice_episodes[/spoiler]