Moody was not shown because the map knows the viewer's intention and only shows things of significance.
Although my answer is nearly a duplicate of my answer on Peter Pettigrew, since this is a different question, I'm posting it twice:
We clearly see that the Map DOES NOT SHOW ALL PEOPLE AT ONCE from the following quotes:
“Ron, I don’t believe it — it’s Scabbers!”
Ron gaped at her.
“What are you talking about?”
Hermione carried the milk jug over to the table and turned it upside down. With a frantic squeak,
and much scrambling to get back inside, Scabbers the rat came sliding out onto the table.
“Scabbers!” said Ron blankly. “Scabbers, what are you doing here?”
And then here:
“The number of times I saw James disappearing under it…” said Lupin, waving an impatient
hand again. “The point is, even if you’re wearing an Invisibility Cloak, you still show up on the
Marauder’s Map. I watched you cross the grounds and enter Hagrid’s hut. Twenty minutes later,
you left Hagrid, and set off back toward the castle. But you were now accompanied by somebody else.”
Now, if Scabbers was hiding in Hagrid's hut, he should have always been visible! So why did Lupin not see him in Hagrid's hut the whole time? There's simply no way to answer there were too many dots, clearly, the only dots in Hagrid's hut at the time were Hagrid's and Pettigrew's!
We also see that the viewer isn't normally on the map:
What did he have to do? He pulled out the map again and saw to his astonishment, that a new ink
figure had appeared upon it, labeled ‘Harry Potter’.
This clearly implies that Harry himself had not been on the map before! (Although here the figure is new, the label itself shouldn't have been that astonishing to him.)
However there are three facts about the map that can answer the question:
One, the map was invented for a specific purpose: Mischief:
Messrs. Moony, Wormtail, Padfoot, and Prongs
Purveyors of Aids to Magical Mischief-Makers are proud to present
THE MARAUDER’S MAP.
Also:
He took out his wand, touched the parchment lightly, and said, “I solemnly swear that I am up to
no good.”
Also
“I’m getting there, Sirius, I’m getting there… well, highly exciting possibilities were open to us
now that we could all transform. Soon we were leaving the Shrieking Shack and roaming the
school grounds and the village by night. Sirius and James transformed into such large animals,
they were able to keep a werewolf in check. I doubt whether any Hogwarts students ever found
out more about the Hogwarts grounds and Hogsmeade than we did… And that’s how we came to
write the Marauder’s Map, and sign it with our nicknames. Sirius is Padfoot. Peter is Wormtail.
James was Prongs.”
These quotes show us that the map was intended for mischief, and specifically, was invented for James and Co. to be able to sneak around camp grounds.
The second fact that can answer this question is that the map is intelligent.
But even as he stood there, flooded with excitement, something Harry had once heard Mr.
Weasley say came floating out of his memory.
Never trust anything that can think for itself, if you can’t see where it keeps its brain.
This map was one of those dangerous magical objects Mr. Weasley had been warning against…
Aids for Magical Mischief Makers…
And by the episode of Snape we see further evidence of the map's intelligence:
“Professor Severus Snape, master of this school, commands you to yield the information you
conceal!” Snape said, hitting the map with his wand.
As though an invisible hand were writing upon it, words appeared on the smooth surface of the
map.
“Mooney presents his compliments to Professor Snape, and begs him to keep his abnormally
large nose out of other people’s business.”
The third fact is that the map can change its appearance to help with the mischief:
What did he have to do? He pulled out the map again and saw to his astonishment, that a new ink
figure had appeared upon it, labeled ‘Harry Potter’. This figure was standing exactly where the
real Harry was standing, about halfway down the third-floor corridor. Harry watched carefully.
His little Ink self appeared to be tapping the witch with his minute wand. Harry quickly took out
his real wand and tapped the statue. Nothing happened. He looked back at the map. The tiniest
speech bubble had appeared next to his figure. The word inside said, ‘Dissendium.’
This is incredible! The map not only deviated from its purpose (showing Hogwarts) it realized that Harry did not understand how to open the secret passage, so first it showed him the wand-tap, but Harry still didn't get it, so the second time Harry looked, it showed him the spell! So this map can realize the viewer's intention and difficulties!
So we know 4 facts from the books:
1)Not every dot appears on the map.
2)The map is intended for mischief.
3)The map is intelligent.
4)Using its intelligence, the map can change its appearance to help with the mischief.
From these four facts we can deduce that the map does not show everybody at once, but rather shows only people who the viewer is specifically looking for
or that the map feels can interfere with the viewer's intended mischief (or the whatever the viewers intention is) with the map.
This is further proven by the dots shown to Harry the first time he uses it:
A labeled dot in the top left corner showed that Professor
Dumbledore was pacing his study; the caretaker’s cat, Mrs. Norris, was prowling the second
floor; and Peeves the Poltergeist was currently bouncing around the trophy room.
And also (GOF):
Out in the dark corridor, Harry examined the Marauder’s Map
to check that the coast was still clear. Yes, the dots belonging to
Filch and his cat, Mrs. Norris, were safely in their office . . . nothing
else seemed to be moving apart from Peeves, though he was
bouncing around the trophy room on the floor above.
In all those cases, the dots shown to Harry were those that would cause an impediment to Harry's purpose (sneaking around).
Therefore, we can answer all the questions "Why didn't x appear on the Mauraders Map" with a simple answer: It didn't affect whatever they were using the map for at the time. Thus there was no need to show them.
This explains why Lupin didn't see Peter until after he joined with Harry and Ron: because Lupin was keeping an eye out only for Harry, Peter was of no significance and thus the map didn't show him, but after he joined with Harry, it became significant for Lupin's use of the map, and thus the map showed him.
This also explains why nobody saw Moody in Crouch's trunk and Sirius or Rita Skeeter in Animagus form: Because they were insignificant for the map's purpose.
This also why Harry didn't notice impostor Moody as Crouch until he tried looking in Snape's office: Since Snape's office was significant for Harry, the map showed Crouch.
This is further proven by this statement of Fred:
“Right,” said George briskly. “Don’t forget to wipe it after you’ve used it —”
“— or anyone can read it,” Fred said warningly.
“Just tap it again and say, ‘Mischief managed!’ And it’ll go blank.”
Now, if there are hundreds of dots on the map, who cares if anyone can read it!?
But if the map only shows what is necessary for the viewer, if an authority figure would use it, the map becomes quite dangerous indeed.