1) I think when the right leg is coming forward, it straightens out too early. I think the thigh should get to its forward angle quickly and then "swing" the calf forward until the leg is straight. Look at how the left leg's thigh is almost in position even before lifting the foot off the ground. The legs should act symmetrically. The left leg and right leg should be practically indistinguishable in how they animate.
2) The thighs seem too short, and the calves too long. The knee should be in the middle of the leg, not the top. Unless you're animating a mutant.
3) The arms (and legs) should animate along smooth curves. The right arm bobs its hand twice just in bringing it forward. For one full walking cycle, the hand should swing back once and forward once, and that's it. No bobbing hands. And the elbows should bend very little in walking.
Basically just look at every joint. The angle formed at every joint should be changing in a smooth curve wherever the joint allows, and should form a smooth cycle for one full walking cycle. Every abrupt change requires energy to change the limb's inertia, but walking has evolved over millions of years to require a minimal amount of energy. The hip should be basically a sine wave: back and then forward, with the change in angle being slower around the time it changes direction. Knee should be kind of a cut sine wave because it doesn't bend forward, only back. So straight, then back, slow, then forward until straight again. Maybe the angle slows slightly before becoming straight, but the knee joint's 1-way nature makes it require less energy to stop its swing forward and become straight, so it doesn't need to slow too much before becoming straight. And because the knee is coming off the hip, the foot moves faster going forward than it does going back because the hip's change in angle adds to the knee's change in angle when moving forward. Right now the changing of right leg's knee angle doesn't have much "curve" to it. It seems almost like a switch: bent at 20 degrees or bent at 5 degrees. It should move gradually from straight to ~30 degrees and back to straight.
That is my guess. I'm not terribly experienced in walking anatomy, but generally things should look smooth at every joint, I figure. The whole goal is to make things look smooth right? Once you do that, hopefully it automatically looks natural if you get the timing right.