The cycle's already looking good! You mention that he could break the cycle and wave and I like that, it would add a nice little moment.
Animation wise, there only a few little spots that stood upon first viewing.
- I like the rhythm of the root up/down movement, there's good weight in that and how it translates into the head for the overlap
- The head feels a bit detached, as if it was IK. Is the neck stretching when the head goes up? You could also have some sideways tilt, it feels a bit locked vertically
- looking at the front view, the hips look like there's a little bit too much Y rotation in there
- watch out for finger intersections through the hips (screen right one, front view; and left one I think too); I would also add a little bit more of an arc to the swings of the arms (they can do a little figure 8 arc when seen from the top); right now they are a bit straight they way the swing back and forth
- could you lessen the knee pop form x16 to 17? And watch out for the other knee, which goes back until x27, then forward for one frame, but then back again to x1 and forward again on x2; in real time it looks a little bit wobbley
- The feet moving backwards feel uneven spacing wise; the moment the foot touches the ground to the moment where it lifts off there should be only two keys, with a linear curve from touch down to lift off. Right now the spacing distance changes and the screen right foot even slows down before it gets off the ground (watch for toe intersections around x4 with the ground); you could also tilt them a bit more sideways around x12 for instance (screen left foot, front view)
- I would also offset his eyebrows and lower the top eye lids a bit, he feels spaced out)
Hope that helps!