Q. Can a gabai leave on a recording device on Shabbos by the bima, so there will be a record of the donations given, when the people are not aware they are being recorded? Why is this any different than the security video recorders installed now at every building, store and even the shul, activated as you walk on the street or into the building?

A. Horav Shlomo Miller’s Shlit’a opinion is that this is prohibited, even when the recorder is left on before Shabbos or has a timer. The prohibition is on the gabai who left on the recording devise and this would include also video recorders when not needed for security reasons.
See Chashukei Chemed and Veha’arev N’a (Shlach) on a similar question where he deals with the payment of the neder that was unlawfully recorded by the gabay on Shabbos.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a