First of all, let me say I did not apply for the Moms Panel this year, just too many other things going on in my life right now, but I did apply for the first Moms Panel and made it to round 2 and applied last year and did not make it to round 2.
I have no idea exactly how the selection criteria goes, but I would imagine the first applicants they weed out are the ones who did not use proper spelling and grammar in their answers. You can love WDW and be quite knowledgable and enthusiastic about it, but if you can't write properly, they are not going to pick you to be on the panel. From reading the DIS for a few years, I have seen a few posters who would fall into that category. After those entries are eliminated, I would guess there are probably certain things they are looking for. They want a well-rounded panel that is going to be representative of all areas of the country (and weren't there even international panel members this year?) and many different types of family dynamics. Obviously within those limits, they are looking for articulate people who are passionately interested in all things Disney and have the knowledge to back up that passion.
After passing the grammar/spelling area, I am guessing that I made it to round 2 the first year for one of two reasons; I have a special needs child and I have taken multi-generational trips, as I know they are really interested in whole families coming together to vacation at WDW. My answers must have been good to make it to round 2, but I also think they had specific things in mind. Once they had narrowed the field down to the 100 or so round 2 submissions, I would guess that's when the real scrutiny came as far as just how well someone can write, and how personable and relatable they come across on paper. I am sure it was a VERY tough job judging those applicants, especially once the round 3 telephone interviews came around. I was disappointed I did not move on to round 3, but once the final panel was in place and I started reading their answers, I knew that Disney had made the right choice.