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.
2004 Ford Crown Victoria Problem Reports
Most Reported 2004 Ford Crown Victoria Problem Reports
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The throttle position sensor (TPS) may fail. Common symptoms of a defective TPS can be rough idle, hard starting, hesitation on acceleration, poor fuel economy, and stalling.
Transmission wear is common. Pieces of broken components are often discovered in the transmission oil pan when the transmission is serviced.