The first season of Magnum was plagued by poor production values, poor acting by the extras (and often the guest stars too), and a "sameness" that made watching episodes close together (as happens when you have a DVD) a little dull. With the second season, all these issues are alleviated to a great degree (although not entirely eliminated), and the show becomes more fun to watch.
It's not that the average episode is written much better - that will have to wait for later seasons, although the last disc in Season two is solid from top to bottom. No, it's that the characters are now in full form and the stories are richer for the interplay between the 4 main characters (Magnum, Higgins, TC and Rick). In fact, the extended universe starts to finally take the form it would keep for the rest of the series, with first appearances by Michelle (Magnum's wife), Agatha (if not the character, at least the actress), and the first of Higgin's legendary half-brothers (Elmo Ziller, from Texas, which allowed us to finally hear John Hillerman's real accent!). Similarly, the shows "feel" more like Magnum, leaving some episodes with bittersweet conclusions, and others without real conclusions at all - like the episode "Mad Buck Gibson" where we never learn if Mad Buck survives his last death-defying stunt. Why not? Well, it wasn't the point of the show, and the show ends just as it should, with Mad Buck appealing to Magnum mano-a-mano and talking him into allowing him to try hang-gliding to Maui.
Unfortunately, I had to deduct a star for the quality of the DVD set. Like all 2-sided DVD's, it's difficult to keep both faces clean, so there were issues with episodes seizing up, or the menu not initialising, etc. Similarly, the presence of the intrusive and extremely annoying Universal fanfare at the beginning of every single episode - luckily the first chapter break occurs right after the theme, but it's still annoying to have to skip ahead every time (Columbo Season 2 has the same thing - what were the Universal execs thinking?!). Finally, there are no extras, except a couple episodes from other shows (A-Team and Knight Rider), although these episodes do set off how well Magnum has aged relative to other pop-dramas made at the time.