Is it common to have wire leading to dishwasher without an intermediary plug?
a 3-wire connection poking out between the drywall and the floor,
  hardwired onto screws on the dishwasher.


The poking out from a gap part is not right - there should be a junction box and cord stain relief. Likewise, there should be a cover for the connection on the dishwasher itself, not exposed live electrical screws. Other than those, it's not uncommon.