I have seen 15 waiver pickups with no corresponding move and only one drop with no corresponding move. How is that happening?

i think some teams moved players to the minors or DL after the draft and had open spots.

Ray is correct. Team owners are moving players to DL and MiL slots before doing their waiver claims. It all comes out the same although it's more explainable if the moves are made in a single transaction.
As long as everyone does their best to keep a legal roster is main thing here. And everyone is doing a pretty good job of that.