Starting with supported, relaxed breathing will prevent most bad habits and playing problems from ever occurring. Trombonists need all the help they can get to keep up with the valved and keyed instruments. A sticky slide robs concentration, builds physical tension, and can destabilize the mouthpiece on the embouchure. Have students rinse slide by sloshing a cup of water through the slide and carefully wiping slide clean, then applying lube. Hold the inner slide up to show students how thin and easily dented the tube is.
Positions are crucial.
Trombonists need the time between notes to move the slide, so they must recognize instantly what position the note is in. Use position drills often to build instant note recognition and make sure students don't need to follow the positions of the person next to them. Teach 2nd, 3rd, and 4th positions by sight as the slide relates to the bell. Know that the slide location appears slightly different from the players perspective than from the side view and different brands have slightly different positions. Finally, remind students to have the slide in place before they start a note.