On the TOS bridge, they had these twelve large overhead screens above
the consoles. Usually they were showing just "screen saver" pictures.

Can anyone list the episodes in which those overhead screens were
actually displaying information relevant to the plot of the episode?

Here are the ones I remember:

Corbomite Maneuver: photography being monitored by Spock

Squire of Gothos: "Greetings and Felicitations; Tally Ho"

Patterns of Force: picture of John Gill

Where No Man Has Gone Before: what Mitchell was reading (I think)

The Menagerie: just in footage from the original "Cage" pilot

Any others?

All of these involved the screen above Spock's science station. Were
any of the other screens ever used to display anything significant?