Jon Chait says he thinks Fred Thompson will "be formidable both as a primary contender and as a potential nominee." In a general election, I think Thompson is going to end up as a case study in why governors have an easier time winning the White House than do Senators. If you combined Thompson's persona and TV skills with a few token gubernatorial accomplishments (cut taxes eleventeen times, tripled awesomeness, etc.) you'd have a bitchin' presidential contender.
Instead, as a 1990s-vintage GOP Senator he has no real accomplishments to his name and a voting record ready to be mined for attacks (voted for three zillion dollars in Medicare cuts, helped Newt Gingrich make adorable children cry) in a way that will help undermine his considerable assets as a candidate. It's not an insurmountable burden by any means but it does leave him weaker than he might be.