Ghosting on 7 segment display
You have a race condition happening. 

When the counter is changing the data presented from the EPROM will be indeterminate and as such LEDs will light at random for a short period.

As such you need to disable the drivers while the data is changing. 

In this case you can use the clock signal from the 555 to control the output enable (OE, Pin 22) of the EEPROM such that it only drives the LEDs during the second half of the clock cycle.

Since you are using a negative edge triggered flip-flop for your counter, you need to invert the output from the 555 to feed that enable pin.

As others have mentioned, you also need some current limiting resistors in the LED lines. You are also asking a bit much of the 139 to power all segments, a transistor or MOSFET drive for the common would be prudent.







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