The machine was displaying an "nd" code, wasn't draining, and would make a grinding noise when the pump ran. After about 30 seconds of the grinding noise, the pump would stop, and the washer would pause the load.
Diagnosis was fairly easy: I drained the water out manually at the filter housing. (If you have a drain in the floor of the laundry room, and the washer is up-slope from the drain, just drain it onto the floor and into the drain.) Next, leaving the drain filter out, I started the washer from where I left off in the cycle. The pump then tried to run dry, and I could easily hear that the grinding noise was coming from the pump through the filter housing.
I ordered the filter, and it shipped quickly. The repair video offered by AppliancePartsPros.com was my exact make and model washer replacing this exact part, so it was as easy as pie to follow along and do the repair. Total time was probably 30-40 minutes or so.
Tip as you remove screws, place them in a small group with all of the screws you take out during each step. For the next set of screws you remove, place them in a small pile next to the last one, and keep doing this so you have a row of small piles of screws in the order of removal. When it's time to put it back together, start using the screws on the last pile you made, then work your way backwards. This should help you keep track of which screws go where.
Final note: I could have purchased just the pump instead of the pump and housing, thereby saving about $50 in parts cost. If you do this, you'll have to remove the old pump from the pump housing, which is just three screws. Before you remove it, take note of the pump orientation on the housing. Mount the new pump to the old housing with the same three screws, ensuring that you orient the pump to the housing correctly. Otherwise, the repair steps mirror those for the entire housing. If you have no issues with the housing, filter, or drain tube, I'd recommend saving the money and getting just the pump (also sold on this site).