Three brilliant debuts occur in The Time Warrior, specifically in Episode One. The first debut is the first thing we see - the new title sequence that was used for for Doctor Who's eleventh season. It was, it is, and, unless Steven Moffat comes up with something even more spectacular for Matt Smith's first series in 2010, will always be my favourite Doctor Who title sequence. The amount of movement, the changing backgrounds, plus the stunning use of the slit-scan process all come together to make a superb sequence that is often overshadowed by the similar, yet simplified, version that accompanied Tom Baker's first six seasons in the title role.
Second, we get to see the initial appearance of a Sontaran, namely Linx. Not only is Linx a well written character by Robert Holmes, but his physical manifestation, from his armour to his potato head to his spaceship, are all thoroughly detailed and well realized. My favourite bit from Linx is his first scene when he plants a flag in the ground and claims "Earth, along with all its moons and satellites" while standing in front of, and completely ignoring, Irongron and his men. That says a great deal about Linx and the Sontarans right there - all other life forms are unimportant compared to the glorious Sontaran cause. It's a character trait that has survived through every incarnation of the Sontarans up until as recently as 2008.
Third is, of course, Sarah Jane Smith. The first six and a half minutes of Episode One is devoted to the the first meeting between Linx and Irongron (the brilliance of the latter will be expanded on in later posts, worry not), so we actually don't meet the new companion until almost halfway through the episode. Sarah Jane has become such an iconic part of Who lore over the years (and continuing today), but it is worth pointing out that the Sarah we see in The Time Warrior in 1973 is so remarkably close to the Sarah Jane we know in 2009. Elisabeth Sladen has given the character life for well over 30 years, and has made her grow and change in a believable and natural way, and the roots of her performance are instantly visible from her very first scene.