The car had 64600 miles on it and the headlights started going out while driving, which can be very dangerous. The problem is in the Light Control Module which is an expensive part (around $500 to $600 + labor).
Problems for specific Mercury Grand Marquis years:
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Most reported 2004 Mercury Grand Marquis problems
The composite (plastic) intake manifold may crack near the thermostat housing and cause a coolant leak. Ford released an updated manifold that was reinforced to prevent a recurrence. No recall was issued for this problem but Ford did extend the warranty to seven years on some models from the date of purchase.