Have f250 7.3 diesel. Have batteries replaced and alternator checked. Having problem with it eratically showing charging then lights will go dim. Then it will show it charging again. Seems to be worse when driving.

Check the wiring on the Alternator leading back to the Firewall. On some models there is a split in the wiring and one side has a fusible link on it. Sometimes the wiring rests on metal parts and wears through from vibration. Check for this and tape the wires to avoid the rubbing.

Ford in the past has put fusible links near the Batteries and when the Batteries are removed, the wires are brittle and possibly corroded. Its just a matter of failing a little earlier from being disturbed than from corroding through. Check all of your connections.

Make sure your Batteries are fully charged. They should be at 13.2 to 13.4 Volts. I know of an increasing amount of Ford products having charging problems immediately after a Battery switch.
Alternators have stopped charging while the vehicles are on the E-way. The charging systems are being disconnected by something built into the vehicle. I suspect the Anti-theft or Battery-saver systems.

I hope my solution helps you.