One problem that I'm sure everybody has run into is what I'm going to call the "comp.unix.wizards" problem. People who have a problem with unix are looking for someone who can help them, and given the choice between a general questions group and a wizard group, they're obviously going to choose the wizards because that's where the smart people are! Of course, this annoys the wizards who created the group for focusing on advanced unix topics.
Here's a trick I've seen used by more than one team: Give your non-technical distribution list the name "XYZ Technical Discussion". Meanwhile, name your internal team communication distribution list something less attractive like "XYZ Infrastructure Committee". Your "XYZ Technical Discussion" list will get the support questions, and people will feel like they're getting a "more direct line" to the technical staff. In reality, of course, the technical staff read both the "XYZ Technical Discussion" and the "XYZ Infrastructure Committee" groups. This is just a trick for keeping external support questions separate from internal team communication.
(Now, by revealing this trick, I risk ruining it.)