It has also been leaking a bit during each load. Luckily I have a big pan under it so it's all contained though.
A google search seemed to indicate that it was a problem with drainage taking too long. The solution was to clean out the entrance to the drain pump.
NOTE: This post describes the steps I took to resolve the issue. I encourage you to read through it, but make sure you read my last paragraph before actually taking anything apart because that might save you a lot of work!
To find the drain pump, I took the back off the washer. In the following picture we see the flexible hose coming out of the bottom of the washer drum into the drain pump.
When I unhooked the small end of that hose I found a paperclip in it. Then I decided to unhook the large end too, so I could take it out and clean it up better in the sink.
After cleaning that up, I felt into the pump and found a lot of junk in it. There was even a dime in it, bit my 7 year old snatched it before I got the picture.
After getting all I thought I could get out, there was still some small rocks and stringish stuff inside that I couldn't really get out. I decided to take the pump out and see if I could clean it better that way. I unhooked the other hose and pulled on the pump until it came out. It was held in by some rubber grommets. I then had to unhook the wire. After getting it out, I noticed on the other side of the pump was a removable cap.
Once removed, it was easy to remove the rest of the junk. I should have done that first!
After cleaning that up, I put it all back together, and it seems to be draining much better now. So far, the leaking also seems to be fixed.
If you notice that second to last picture, though, you'll notice that there's a really nice big cap that would have been real easy to unscrew and clean out the junk if only I had opened the washer from the front! Looking a little closer, I believe the front might actually come off. I'm not going to take it off now that I've got it all fixed, but if I were you I would try removing the front instead of the back for this project.