The first episode of the series wasn't without it's problems, but it was a fairly good start to the series. The Bad Beginning Part Two, however, while not perfect, is an improvement.
Now, there are a couple of problems I do have with the episode. K. Todd Freeman's role as Mr. Poe still didn't do anything for me due to how inept the character is and while the pacing is slightly better, it did drag a bit in the beginning.
That being said, there are still some good elements. The child acting, while not great, has been getting slightly better and the rest of the actors has been fairly good so far with Patrick Warburton continuing to shine in his narration due to his deadpan delivery and Neil Patrick Harris is as fun as ever as the sinister Count Olaf. The music score fits the atmosphere very well, the directing is still superb, and the cinematography is still well crafted.
Overall, while not perfect, The Bad Beginning Part Two is an improvement over the first episode.