As for #1: How about a new ideas post-it board? Create an area that is highly visible in the work environment. As ideas are discussed slap a reminder note on a sticky and put on the board. Keep the board partitioned into categories (ie UI, performance improvement, etc.). A responsible member can take charge to transcribe these to a full wiki, when detail needs adding or the idea is good enough that it deserves some true effort spent in design.
As for #2: If your team has trouble staying on target, then definitely the mtg organizer must take the time to prepare an agenda and adjudicate conversations stay on topic and insist that meeting ends on time. Leave the meeting knowing who must do what.
As for #3: Someone must lead the charge, find examples of the kinds of documentation and specs that you like to see and schedule some time with the team to review and discuss.