2000 Taurus misfire, etc.....
I've had seven Tauruses from model years '97 up through a 2000. Try the following:
1.Check codes first (OBD II). Take care of those problems(see #2 & #4 below). Cylinder misfire should show up as one of the codes. After resolving code issues, clear the codes.
2.Perform tune up as required. (Also see #4 below)
3.If you are going to pay labor to remove and replace a heater core, Replace the core vs. flushing it and taking a chance. Cores are fairly cheap.
4.Of the seven Tauruses I had, five of those had to have the coil pack replaced. That was the main cause of misfire. Misfiring means that the plugs are not getting spark at the proper time, or not at all, and raw gas has probably ruined the plug(s), and should be replaced.
5. Check for codes again, and so on.....
Good luck with your repairs.