I'm not sure we'll be seeing much of Katara from now on. Korra appears to have mastered her water bending already, although I'm sure she did instruct her.
Yup. As we saw in A:TLA, the training cycle goes air, water, earth, fire -- or in Korra's case, water, earth, fire, air (and so on for each new Avatar -- note that the Avatars themselves cycle through the nations in the same order, for instance from Kyoshi to Roku to Aang to Korra). The episode opened with Korra completing her firebending training; and since she's Southern Water Tribe by birth, naturally waterbending would've been the first skill she mastered. And she is 17 years old, so she's much farther along in her training than Aang was when we met him. So she's completed her studies in the other three disciplines, and air is the only one left.
Also, Master Katara is played by Eva Marie Saint, who was billed as a "Special Guest Star." That probably means we won't be seeing her regularly.