Well, I gave it a bit more thought...
Instead of what I suggested above, lets say you leave everything as is and implement the Thumbs Up and Thumbs Down vote mechanism. You make the Under Judgment system more lenient or you leave it as it is, this way people who are submitting their first flashes for the first time can get a chance to be seen by the mainstream crowd of Newgrounds.
Now in addition to the Thumbs Up / Down buttons, or the absolute vote buttons, you introduce a button called the Shaky Hand - Representing the viewer's inability to make an absolute vote. Choosing this button will display new buttons equivalent to the current 1 / 4 buttons.
Now the system will keep track of which of the three initial buttons were chosen in the first vote during Under Judgement. The flash submission will be treated normally if more than 45% of the clicks correspond to the absolute vote buttons. Now, if the Shaky Hand button is chosen significantly more times the system should signal the flash and put it under a "Closer Observation" status.
Once it is in this Closer Observation status, review viewing will be enabled for the flash and the system will now keep closer track of the moderate votes. If the majority of the moderate votes correspond to the 1 or 2 votes, the submission in question will be flagged. If it has a significant Thumbs Down vote as well, the flash will be eliminated. If it has an near equal or significant Thumbs up vote, it will go into a Near Death status. It will be up to the next few votes to decide its fate.
Meh, so how's this for a suggestion?