I recently took over managing an organization in a mid-size company. From what people have told me, the organization felt really intimidated asking questions to my predecessor. To fix this, I've started a campaign to really push for an encourage questions and open communication. I've dedicated 30 minutes for every town hall for Q&A, and I've given people the option of submitting questions anonymously and told them I would address every one. I've told people that communication is an essential part of a healthy workplace, and they should always feel comfortable asking questions, giving suggestions, expressing concerns, etc.
Well, my first town hall went fairly bad. There were a few real questions submitted (like "how concerned should we be with the poor quarterly earnings report?"), but there were also a slew of inappropriate questions. Some of them were "what is your mother's maiden name?", "what is the name of your childhood pet?", and "what was your high school mascot's name?". When I finally got to "how many teeth do you have?", I had enough and abruptly ended the meeting.
Because these questions were submitted anonymously, I don't know who exactly wrote them. What are strategies I can take to continue to push for open communication, but convince people to take things seriously and professionally?