One of the cool things about series two of Red Dwarf is that - quite frankly - it feels like the second half of a full-length season. The writing is amazingly consistent, feeling like an extension of season one rather than a whole separate season. In fact, one episode's premise later showed up in an episode of Star Trek: The Next Generation
Fortunately, this is where the universe gets a lot bigger for the crew - the effects budget for the first series went into model work for the main ship; this time, with a little more money, the crew gets off the ship in a variety of ways, whether it's by shuttle (Kryten, Thanks for the Memory), time warp (Statis Leak), virtual video game (Better Than Life) and interacting with their parallel selves (Parallel Universe).
Fortunately, this series also begins laying some ground as to the future - most notably, introducing the character of Kryten. Although David Ross plays the role relatively "straight" (at least, as straight as a science fiction comedy can be), he doesn't take on the full-on neuroses that Robert Llewellyn would later bring to the role. In fact, the addition of a fourth character at this early stage brings a whole new dynamic - and much of this series seems to begin several key plot threads. Rimmer's almost self-destructive neuroses are played to comic effect - so much so that his later "redemption" makes it seem the series is about his character. (In fact, series two is where Lister's, Rimmer's, and Cat's characters begin to gel and solidify into the people Dwarf fans know and love)
In fact, I would argue that this series contains the first real masterpiece episode, "Queeg". (Yes, that is a Caine Mutiny reference). When the Queeg 5000 battle computer takes over for a seemingly ineffectual Holly...well, this episode is the first "great" episode of Red Dwarf. Sharp dialogue, clever writing, and an ending that still surprises after multiple viewings.
Plus, it shows Norman Lovett doing what he does best - kicking bottom and taking names.
But the best thing I can say about Series Two is that...well, if you watch Series One and Two in sequence, it beats out the best season of any American show. Red Dwarf is hitting its stride.
And now, a special treat: the "Tongue Tied" video that appeared in the beginning of Parallel Universe, for your musical entertainment: