Uniform 1px outlines, bit strange/repetitive backdrops and minimap tiles (placeholders?), straight color ramps. (Also, watching the video it might be a good idea to make the sidewalk behind the sprites a bit darker, which makes the scene read better and the sprites stand out.) I'm seeing right away the art in this game could be greatly improved.
But on to the edit. You should go back and focus on the execution of the still frame of the sprite before making the leap to its animation.
I know that it would take a whole lot of effort to revamp every piece of that art to the extent that I revamped this sprite unless you know your way around it, but there are still things in this edit that could be implemented without a style overhaul--in this instance, the forward-leaning pose, the individualized head and facial expression, new position of the hands and arms--but the pose tweak is the most important thing. You could do a different pose than the one I used and you probably should, but the point stands. It's the basis for an animation, so it should look animated! What you have there is stiff and upright where it has great potential to be exaggerated (and this sprite also has balance issues carrying the weapon like that). Ditto for the zombies, soldiers and boss sprite.
The in-game animations look a bit limited for similar reasons, even for very few frames, because it's mostly the arms and legs that seem to move and rotate, even in broad powerful weapon attacks! They need stronger
lines of action. Aside from that, you could study weapon swings, punches, kicks, whatever you'll use, from real life and from beat-em-ups with some well-done animation. I'm looking at the promo art and you could pull these kinds of poses and animation off! You just need to have some forethought however.
Other things: Features were exaggerated a bit, like the hair, and the aforementioned stance, to contribute to the character's individual silhouette. (silhouettes example: remember
this?) If these sprites aren't templates where you mix 'n' match parts, why not? Each sprite could use some individuality, or they become harder to tell apart.
I felt that the palette needed unification so I went for a "theme" color to stand out, in this instance, yellow-green for the gloves as well as goggles. A good dark, contrasting color was used for the rest of the sprite--dark grey, which even makes it into the face, and then maybe some accents. In that sense it has the colors and value range of maybe an 8-bit sprite, which makes it easier to read. Finally a colored outline ties it all together. Also note the tints in the face which mirror real faces.
Also some possible weapon positions indicated by those faint lines, if less straight lines is what you want--a tradeoff between showing the heavy weight of the weapon or the strong grip holding it up. You decide.
As for the run animation, I'm not too experienced myself but do take a look at
Ptoing's walk and run cycle chart. If possible, also find a copy of the Animator's Survival Kit but only if you really want to look into that stuff, movement cycles and such.
I hope this post delivered.