When I have students Peer check papers we are going over as a class, I have the "checker" write his/her name @ the bottom of the other person's paper. As we go through I use the scoreboard. IF it becomes clear that something needs addressing during the corrections, we would appropriate WBT techniques and "Teach-OK"
As for the inquiry piece, think it melds well. Using the 30-45second mini-lessons keeps ME focused on having students driving student learning. When I need the attention of the class..."CLASS- YES" and I will use the scoreboard while they are working. During Project based learning and times when they are going to be working together on a task I might say something like this:
Class...when I give you the signal you are going to work on <whatever they are going to work on> The scoreboard is, of course still in play. Turn to your partner and tell them how excited you are to to <what ever the activity is...>"
Today I read the WBT piece about oral essays. THAT is a great piece for science, I think. While I will be doing math this year, I am going to pull that into what we do each day.
I have even used the scoreboard during Standardized testing...Students know they must maintain absolute silence during the testing...and sometimes seeing that + or - point go up gives my students with high distractiblity just the oompf they need to stay focused (or refocus) and make it to the end of the testing section.