Why (in some synagogues) does the shatz (leader) put on the talis during mincha of Shabas, before "Vaani s'filasi", rather than before the start of mincha?
As Gershon Gold notes in his answer, Shaare S'shuva says this is because when we say "Vaani s'filasi" is a time of ratzon. And as I note in a comment to that answer, Taame Haminhagim says that it has to do with the words vaani s'filasi: a talis is connected to t'fila. But neither of them answers why we wait and put on the talis during mincha rather than before: after all, we don't need a talis until (let's say) "Baruch sheamar", yet we don it at the start of shacharis.