Having only judged 26 contests in the past three years, I don't have the full range of experience as some of the other posters, but I can also say that I have not seen judges only taking small bites so as to have more to save for taking home.
I'm also a certified KCBS table captain and I have never seen any judge nibble an entry. My wife, who is also a judge, has only seen it once.
Also, keep in mind that that you don't need to take 3-4 bites to know what something tastes like- do you take 3 big bites of undercooked chicken/pork before you decide it's bad? I think not.
As someone else noted, if you eat all 24 entries in a contest, you will be too full to do a good job, so all the judges I know pace themselves to be able to focus on judging accurately.
Finally, to those who expressed the idea that no one would want to eat leftover BBQ entries, how many of you just throw away all the remaining meat, once you've built your boxes? After all, it's now "leftovers".
BTW, I would say that about 50% of the judges take food home- the rest just toss the food.
Both cook teams and judges put in time, effort and money to support competitions and for the judges,being able to take home some of the really good BBQ we get to judge is a benefit, I would be sad to see go away.