A good start for a series
I liked this video, not the best sprite video ever, but a really good video indeed. Here's some tips on what to do on the next flash of the series.
A. The voice acting worked pretty well, not sure what software you used in order to place the voices in the video, but there were times that they sounded....staticy. I made up that word, bow down to it, but you get the point, they were gargled and maimed voices at times, but they were fine most of the video. The voice for old toad guy, didn't work out really well. I don't mean to be a jerk, but it just wasn't the right voice for that character.
B. Somebody said earlier that you should remove the gray cells around the characters, this would do wonders for this flash. It may take a little more time, but the more time and effort put into the video, would make it that much better.
C. Animation was wonky a little. I understand adding in certain objects into a sprite video can be weird, such as mario holding a gun, but you need to make sure you get rid of mario's hand while running with the gun. You can see him running clearly with both hands, while the gun just bobs up and down, take a look and it will be obvious. You did a good job with Luigi, and Bowser just needed his gun to be on his hand, not off to the right of it.
D. The plot is simple, I like that, but one thing you need to be careful of is with zombie movies, people tend to basically do "and they were all zombies in the end, everybody died, boohoo" Although I wouldn't say "and they lived happily ever after" but go with a zombieland, or Shaun of the Dead approach where they adapt to living with zombies (Shaun of the Dead is a little extreme, but you get the point)
E. Please tell me you planned for the video to be 666.6 seconds long, if so, I bow to you.
Good start, hope you crank out the rest of it :D