The 'refresh rate' of the displays is driven by the IRQ line (TP5 on the MPU). This should be around 1kHz (30us low and 70us high). If it isn't getting generated correctly, you can see the digits refresh individually like that.
First step would be to check TP5 with a scope or logic probe. If you're not seeing a 1kHz signal, then trace back to the components involved in generating it... Any corrosion around IC5, IC11, or IC25?