Ford MAF's are built with hot element sensing (Bosch AFAIK).
Basically current to flows through the sensing wire to maintain a fixed temperature. As air flows past the wire, it removes heat, and so more current is required to maintain the fixed temperature. The change in current indicates the magnitude of the airflow, but it's not a linear relationship.
There is some serious active analog signal conditioning circuitry built inside.
So the supply voltage runs the works inside, and it calculates a linear output signal that is proportional to the airflow.
Notice from the wiring diagram above that the MAF power source is switched, fused 12V, reference voltage is 5V as described. Either one could be an issue.
The pipe routing upstream of the MAF can be critical too, the stream flow to the MAF should be uniform, or at least consistent.
How (and where) are you measuring the signal?
Are you using the stock EEC-IV setup?
Output impedance of the MAF circuitry is fairly high, so any loading (from analog meters, or auxilliary circuits) can degrade the signal.
Does the TwEECer let you display what MAF the voltage ECU sees?
I use an OBD interface to a laptop that lets me monitor and graph various ECU signals, can be very useful for troubleshooting.
Carter