The fix had three parts:
The red arrow marks a piece of felt he placed where the top and bottom sections of the window come together and stuck on there with a bead of silicone. The orange arrow points to small pieces of foam wedged into the track. (The spots I plugged with paper towels after discovering the leaks.) Our happy idiot cocker spaniel can also be seen in the lower part of the window. (Placed outside so the man could work in peace.)
The last part of the fix involved more foam wedged in the bottom corners.
While he was here I also mentioned that the plastic in the middle of the window in our laundry room is cracked as well. He took a look at it and told me he'd be putting in an order for them to send us a replacement. (The whole bottom half since that plastic can't be replaced separately.)