Battery was questionable under load test when car was bought - replaced it.
52500 miles - Entry keypad; one key died. Not fixed yet.
53000 miles - Car started making fog horn noise, apparently from the air filter box. Replaced IAC motor and cleaned MAF sensor at the dealer (I was pressed for time, and knew I was going to get robbed), $330.
I wanted a safe, reliable, durable, long-lived cruisermobile with not many miles for not too much money that could haul a lot of people and stuff plus possibly tow a small trailer or boat. The Grand Marquis is all that - I would have been happy with a plainer car or SUV - and in the internet, magazine, and people research I've done, just about everybody likes their MGM/CVs and their value. Only drawbacks are the storied exploding gas tank, the RWD in snow, and the intake manifold.
After some research on the gas tank (and putting in the fuel tank shield, $200) I don't think it's an abnormal risk (a 75mph rear end collision isn't good in my Geo, either).
For the RWD, I've got the best all-weather tires I could find (Touranza LS-Ts), traction control, ABS, and 300 pounds of sand in the trunk. We'll see.
I didn't find out about the 4.6L's intake manifold problem (it's plastic and apparently can crack, leaking coolant into the oil and potentially destroying the engine) until after I bought the car. I think that GM's 3.1L and 3.8L engines have the same problem in used cars (in 95's to early 2000's?). Something to watch for, and a reason to look under the hood weekly or so. No one I talked to mentioned it, and it's not written about much, so I don't know how often it happens. Maybe it's not a significant risk.
The car drives likes an SUV, big and creaky. Very good on the highway, and OK in the city. Mileage is about 20-22mpg for the mixed driving I do. It goes as fast as you want it to, and it accelerates fine; I've never had to floor it yet. Radio, CD, leather, all the fancy stuff is fine.
I'm a little disappointed that I've had two failures so soon after getting the car, and both seem like common failures for this model car. The IAC was supposed to be more of a 1999 problem than 2000, although apparently it's pretty common across model years. If Ford really is trying to beat the Japanese, you'd think they'd fix this kind of constant trouble spot. These cars are supposed to last a long time (e.g. "MGM taxis drive for 400K miles", etc), but only if you follow the maintenance schedule. I'll update here from time to time.