heater will get stuck on high heat at some point in time. Probably pretty soon if it hasn't happened already. called the DCCV
low power mode is actually a good thing although you will not think so when it happens. It reduces your power giving you just enough to get home or to the shop. I discovered what it was when 4 coils went bad this summer. A light comes on too but I don't remember which one.
Congrats on buying the 04 it is a great car. With car prices down right now I'll bet you got a good deal on it too.
Valve cover gasket problems were pretty much fixed on the 2nd gen LS, you have an extended warranty of 100k miles or 10 years. Coil failure due to water contamination from seal is also covered.
I would call your local Lincoln dealer, give them your VIN and see if your car is covered by this extended factory warranty on coils, plugs and valve cover gaskets. I had one of the kids that used to post on here who lives near me do that when he found oil in a few of the plug wells and he was covered. Saved him the time and money of doing it himself.
If you do a search for "program m707", you should see a thread started by me with a scan of the letter I got from Ford about this problem.
Good luck and enjoy the new car.