Off the cuff.
Clean the edge Connectors
Check the voltage off the power supply.
Pull the board with support under the board gently but firmly press the chips down.
If it's still doing this. Try replacing the ram and see if that clears it up..
I came up with the same issue and was stumped. It's a downer when you find a post with the issue but the resolution is never posted. So I needed to make sure this is resolved for the next person who has this issue. I did some more searching and found this old post on the JAMMA+ forum which helped me solve the issue and has a lot of other good MC troubleshooting information:
Symptom: The aiming cross left a trail, and the red arrows and cities had the same flashing coloured box around them thanks to Mike Coates for this
Diagnosis: Some experimenting with MAME revealed that when the cities were drawn it read what was behind them first, as did the moving cross so it could be assumed that the reading of video ram was wrong. However, the video ram had already checked out OK, so it had to be something that was only used for this feature. Missile Command has a couple of hardware blitters that read pixels from separate video banks, and the bank causing the problem returned 2 bits via P7 (74153), R7 (7475) and R6 (74125). P7 checked out OK, but R7 and R6 were not so easy to test
Cure: Replacing R6 and R7 solved the problem. Note: have also seen this caused by a bad output on pin 6 of the LS00 at location C5
Additional symptom to add: In test mode, the white crosshair would leave a white trail.
For me it was R7 (74LS125) which I confirmed by piggybacking a good one over the suspect chip.
Thank you Mike Coates and "IronGiant" wherever you are ......