"So, let me ask you - Do you know anyone, anyone at all, less threatening than this man? . . . Less threatening, and yet secretly, inexplicably guaran-damn-teed to fall ass-backwards into the lap of success?" - Winston summarising Harry in "The Trouble with Harry"
Harry appears to possess some infinitely redeemable marker, a 'get out of jail (with my help) free' card, given him by Chance and the only one of its kind. What could make Chance feel this way is never made clear in the series. Whatever his shortcomings, however, Harry is willing to face his fears, which is a form of bravery.
Harry is, seemingly by serendipity alone, a catalyst, as things from a mass break-in at the team HQ to a new level of understanding between Winston and Guerrero happen when he's around, often due to seemingly innocuous remarks or actions on his part. He is a klutz, but one the universe is clearly bent on protecting, as the above quote by Winston makes clear. Harry does his best at all times, and shows flashes of surprising bravery when clearly overmatched.
He would in all likelihood have continued to recur had the series gone into a third season.