Welcome

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"On my way home the CEL comes on."
Go to Advance or Autozone and get it scanned (free service) and post the CEL codes (even though it is off now).
"Today, I noticed it wanted to stall twice more, both times as I had deaccelerated from 50 to about 10... when I pushed the gas again it just hung for a bit at 2k rpms and slowly creeped up... once it got to 2.5-3k rpms everything was normal.
........
It also straight out stalled twice more, both times where when I was accelerating fast and had to come to a somewhat abrupt stop and make a turn at 3-5mph. Just flat out died both those times."
Change fuel filter. Clean (change) IAC valve. Clean MAF sensor.
"Symptom: â??missesâ? during light acceleration @ ~ 1-2k RPMs, no problem wide open throttle / stalls during deacceleration and/or at idle"
Spark plugs or wires, IAC valve. Also do a throttle body cleaning. Pour a bottle of fuel injector in the gas tank.
Might as well change the oil and filter and air filter (if dirty).
"
Symptom: no dome light while driver's door is open. (dome light works normal with other 3 doors.)
-check rubber switches / spring by door (a&b pillar), use wd40, push in/out."
Yes.
"[side note: no chime for â??lights onâ? when lights are on with door open / key out. car probably thinks door is closed at all times? seems logical.]"
Yes, do the same as above.
"Battery light in dash goes on/off for seemingly no reason (on 10 or so minutes of operation, off 10 or so, repeat)"
Check cables from battery terminals to alternator and battery to ground.
Check battery. Engine off. Headlights on for one minute. Voltage across battery terminals should be 12 to 12.5.
Alternator test. Engine running. Voltage across battery terminals should be 14 to 14.5.
"Gear shift "orange marker" stuck on first gear, doesn't illuminate
-needs new kit? wasn't there a recall on this?"
Yes, there is. If it is not covered, just wrap a thick copper wire on the gear stalk (just above the transparent plastic RND21)so that you can see what gear you are in.
Bulb is probably blown, (not covered by recall). Just change it, Autozone.com has some good pictures.
"Pulls left slightly
-probably just needs an alignment"
Check tire pressure first.
Good luck. Do these cheap and easy ones first.
Edit. Most how-tos are here.
http://www.contour.org/ubbthreads/showflat.php?Cat=&Board=v6maint&Number=958650&page=0&view=collapsed&sb=5&o=31&fpart=1
IF your Mystique is covered,
"POWER TRAIN:TRANSMISSION:AUTOMATIC:LEVER AND LINKAGE:FLOOR SHIFT Recall Number: 98V233000
Dates Manufactured: JUL 1994 to JAN 1998
Number of Vehicles Affected: 175000
Date Owners Notified On: N/A
Vehicle: 1998 Mercury Mystique
Defect Description:
Vehicle Description: Passenger vehicles. The floor shift automatic transmission control can be damaged if subjected to certain interior cleaning products. The gear position indicator can deteriorate and not correctly indicate the actual gear position.
Consequence of Defect:
This condition can result in incorrect gear selection.
Corrective Action:
Dealers will replace the automatic transmission floor shift control."
Shift position lever thread.
http://www.contour.org/ubbthreads/showflat.php?Cat=&Board=trouble&Number=1069992&Forum=trouble&Words=credit%20card&Match=Entire%20Phrase&Searchpage=0&Limit=25&Old=6months&Main=1068894&Search=true#Post1069992