Is there a missing ground wire in my pedestal service circuit?

You are being written up for a missing Equipment Grounding Conductor (EGC) which is the ground wire that goes with hots and neutrals in every circuit or feeder.

The thing between this meter-main and your house is feeder not service wire. Above the meter is service wire. Feeder requires EGC, service does not.

What I see

is 200A service coming from the top.

I see a bare wire that is part of the Grounding Electrode System which bonds the meter-main chassis itself to local grounding rods. However this is not an EGC ("ground wire") and does not go anywhere an EGC needs to go.

I see the main feeder going into the lower pipe in 3 wires. I see no ground wire (EGC), so yeah, the inspector got it right.

Fire your electrician. What were they thinking?

If the power company installed this feeder, that would be why. They follow a different codebook (NESC) and they're not used to working in NEC rules. They make this mistake all the time.

Some people think that if the pole has a ground rod (GES) and the house has a ground rod (GES), they don't need a ground wire (EGC) also, because there's dirt between the two. Um... dirt doesn't conduct electricity that well :)

What to do

You will need to add an appropriate sized ground wire to the pipe. If the hot wires are exactly #2/0 Copper or #4/0 Aluminum, you can use a #6 Cu or #4 Al ground wire. (However, if the hot wires are larger than that, the ground must also be larger, forcing you to #4 Cu or #2 Al).

The added wire can't exceed conduit fill limits. The ground wire can be bare if it's copper, which helps with conduit fill. It's OK to use aluminum hots + copper ground.

You can fish just the wire if you can successfully get a fishing tape down that conduit with the wires in there. If not, you'll have to pull the 3 wires and then pull them back in with the 4th wire.