I installed my new Ultra Seal Dryer Vent today. The vent came without an attached duct. I was hesitant to rip the duct attached to my current vent in case there was a problem installing the new vent. So I bought a piece of ducting at the local going-out-of-business hardware store for about a dollar. I trimmed it to 12 inches long, and siliconed it into the vent.
Dryer vent duct
One thing I noticed was that the plug was not seating flush, and left a small gap through which air would leak. I thought maybe I made a mistake in buying this if it wasn’t going to seal well. Upon closer inspection I noticed that there was a small bit of ‘flashing’ on the plug piece from the molding process. I trimmed this off with a sharp knife, and now the plug seats well and there is no gap.
I pulled off the old vent, and saw there was no insulation below the vent hole. There was some above, and some to the side. So I took the time to shove some insulation in there. I also used Great Stuff to seal a gap between the dry wall and the floor. I take it this is where I have had mice coming in.
Dryer vent hole
I spread a bead of caulk around the hole on the outside, and shoved the vent into place. Six screws, and the unit was mounted. Dryer vent
I went back inside, re-connected the dryer hose, and pushed the dryer back into place. Done.

Afterword: My wife commented afterwards that the new dryer vent works. She said that on cold days, the inside of the dryer used to be like an ice box. But with the new dryer vent, it isn’t. Awesome!