What effect will one wrong sized tire have on a 2002 E-350? Obviously all the tires will be be effected and need to be replaced, but what else should I be concerned about? Brakes? Rotors? ABS sensor? Transmission? Differential? Suspension?

 

Let's say that wrong sized tire has a much smaller diameter. That wheel is going to spin faster than the one on the other side. If it is the driven axle the differential will work overtime.
No problem with the transmission.
The brakes could be affected but it would take a long time to show as increased wear. I would be more concerned about uneven braking power and loss of control in extreme situations.

If the difference in the diameter is very small, let's say 1 or 2 % I would expect very little problems.

 

The ABS will be affected if it is 4 wheel ABS. The ABS does not only detect wheel slippage, but it detects differences in revolutions of each wheel. If one is larger or smaller in diameter than the others, the ABS will think there is a problem and either not work of falsely activate.

 

I have to agree since the wheel that is going slower will provide a slower speed signal to the ABS system and it will be perceived as locking up causing the ABS system to try to make corrections for a condition that does not exist.