too many to really name, so i've done an edit of how i feel he should move.
remember, up, down left and right are only *implied* directions in a 2d envionrment. you still have to deal with perspective and most importantly, lnes that are not strictly verticaland diagonal.
also, i would try to avoid using the cardinal directions as much as possible to make things feel more lifelike. when your motion is dictated by quarter-clock position, the end result is rather mechanical. Unless it' s absolutely neccesary, i'd avoid using the 3-6-9-12 (think hands of the clock) positions. Instead, us the 4-7-10-1 position. this will probably look and feel more natural.. true, they're a bit harder to work with, but i'm pretty sure you can do it if you play with it for a bit.
It didn't make sense to me for him to swing a two handed weapon with one hand, especially if he begins the motion using both hands. unless he's swinging a baseball bat, in which case the motion would be entirely different. As such i had him hold onto it, because you need power for the follow-through of the swing as well or else he's risk losing contrl of it, or worse, letting go of it altogether.
my edit.
Swinging a sword requires a lot of body movement. just keep that in mind. I stated in some other thread, don't think of the sword moving, think of the person movin the sword. all of the sword's motions should come secondary, and more naturally. the body would also pivot - all the 'power' of a swing is in the hips - pivot them! you see what i mean? it's a dedicated action! if you're going for a more baseball-playerish style and approach, watch some baseball players. see how they move; even then they move their entire bodies in the swing. gives it more power and motion.
I really should start working on my own animations, they still need a lot of work :\
i've learned a lot just editing other peoples stuff
