One problem related to engine has been reported for the 2004 Ford E-350. The most recently reported issues are listed below.
I have a Ford E-350 super duty van that has had drivable problems since it was new. After many trips to dealerships I was told that there was no fix at this time and Ford should come out with a fix in the future. The engine dies when hot at times causing hard braking and loss of steering. At 100699 miles, just 699 miles out of warranty the engine quite running when hot. If it sits for 6 or more hours it will restart and run for only 20 minutes. Ford told me it was no longer under warranty and would provide no assistance.