Animation is not always smooth, and some peculiarities

I understand this is probably just a basic example to demonstrate key concepts, but how would one go about solving these issues:

• At 10:26, the character jumps briefly into the standing position. I'm guessing this is because the beginning of the turning animation clip is the character standing? If I hold down W + A/D and basically just keep turning forever, every time the 7-second turning animation clip finishes, the character goes back into a standing position briefly before continuing the loop.
• If I keep turning forever, a weird thing also happens where the character starts sinking into the ground. Is the character possibly slightly beneath the ground at the 7-second mark where we trimmed the length down to? 
• When going from idle to left/right, the animation looks a little odd if a specific leg is forward; it looks like the legs freeze in place while the whole character tips to the side to begin the turn.
• When trying to go quickly from left to right directly or vice versa, this results in a jerky animation.