What you remember, might be a feature in another program than Finale.

There are several programs with a such “drag-copying” feature.

1) If you have, in a single staff, an expression from a “no-Score-List” category (e. g. a dynamic), then you can quickly copy the expression to the staff above/below by holding down the correct modifier key (Ctrl? - Alt?), and hitting UpArrow/DownArrow.

2) If you just added an item (an articulation, an expression, &c.), you can add the same item again via the metatool {Add Again}.