First of all, let me say it is not a question of using an incompetent mechanic or vice versa. This car is truly a lemon. Ford darn well knows this too. I came across this Mystique when my girlfriend bought one 3 months ago. This Mercury has given her nothing but problems. I'm glad I came across this site, because I thought I was going crazy. I would say I'm pretty knowledgeable on cars and maintenance. I've been working in retail auto parts for over ten years, & tend to do most of the work (from oil changes to tune ups) myself.
But let me tell you, the first problem was the stalling! It would stall for no apparent reason. The (mistake) stalled on her on 3 separate occasions; twice on the freeway (highway) & once driving on the streets. No matter what I did, I couldn't find the stalling problem. After a week of troubleshooting and brainstorming for possibilities, it was found to be a problem within the fuse box under the hood. The wire going to the main fuse was burned & melted.
Then the transmission started to act up. It shifted like a brute... the o.d. light in the dash started flashing? It had a mind of its own, stopped on its own & worked again fine, like nothing ever happened.
The next thing is the temperature. This car runs very hot; the needle in the temperature gauge almost hits the red before the fans are activated. I changed the thermostat, flushed and replaced the coolant, changed the coolant temp sensor, but still it runs the same (as before). And no; the gauge or sending unit are not defective.
Then the blower fan only works on high, not on low or med. but high. Aside from the minor things like water leaking into the trunk, the cup holders breaking, air vents breaking, dull headlights lenses, etc. this car is a freaking total nightmare!
To those whom have had no problems with this model, let me tell you, you guys are lucky; sooner or later it's going to start acting up.
Its odd that you didn't fill out the mileage part of the survey. Is it that the car might be over the mystical 100k mark? If it is, you have no one to blame, but yourself. Almost every Ford seems to have electric problems, which only get worse with high mileage. Maybe you shouldn't rely on cars the girl friend buys.
It's a 12-year-old car, so all bets are off. All the things you mention are easily fixable.
Hard shifting: change transmission fluid and filter. It's supposed to be changed every 60,000 miles, and Haynes says 30,000 miles.
Temperature: you're on the right track by flushing the system, changing the thermostat, and checking the sensor. Replace the sensor, and also check to see that the fan motor isn't corroded, or doesn't have some blockage. It's just something you haven't thought of yet.
The blower fan is either a fuse or a rheostat switch. Use a voltage tester.
Dull headlight lenses: use rubbing compound on the plastic lenses to polish out yellowing discoloration.
Broken cup holders and air vents: get real.
These are all common issues to be expected on a 12-year-old, high mile, used car. If you're not up to it, it might just be better to buy a new (er) car and make the payment.
Actually Ford made a total piece of junk. The car has a BIO-DEGRADABLE Wiring Harness! Fact of life, the wiring harness's disintegrate after a few years. Ford recalled to the original owner only, 100k miles or 10 years. The cars have shorted wire everywhere under the hood. Replacement harness is the same crap and is $2,000 to install.