The problem with Harry is that he was supposed to be two things at once. On one hand, we're told that he's brilliant, graduating at the top of his class, with a gorgeous fiance waiting for him back home, and a choice assignment on the senior staff of a state-of-the-art ship right out of the Academy. On the other hand, we're told that he's green, naive, inept with women, and unready for command (even after seven years in the Delta Quadrant!).
Which Harry did you get? Whatever the episode (or, the scene within the episode) required. It's no wonder the producers couldn't remember his character's background or ethnicity; Harry Kim just wasn't a fully thought out character.