I see you reading! Post and help out! 
Okay, what clues are we still befuddled about? fellowtraveler had an initial list. I'll put that here, and add in the others we discover.
Overall:
What's with the references to 4, and counting to 4?
Crow's Nest?
Maddie Hayes? - A character from Moonlighting. Maybe an homage to the fact that the puppetmasters are moonlighting as puppeteers?
Episode One
Potential (or unsolved) clues:
(a) "Instead of Central Park we call it Pentral Cark";
(b) "Instead of calling it window sill, we call it window sell. Sill, I-L-L, sell, E-L-E";
(c) Belly jeans
(c) The chinese finger trap
(c) the Crow's nest in general;
(d) the "code of all codes" drawing that Mulligan makes. - Is this a drawing from point to point connecting the clue locations?
Episode Two
Potential (or unsolved) clues:
(a) the flag stolen from a merchant vessel - I think this is the layout of the ballfields next to the lampposts.
(b) switching Tutty with a potato. "Potato". Is this an anagram? To atop?
Episode Three
The Columbus Circle station has little decoration. It does have a big compass on the floor on its south end and a big colorful wall. I've walked through it several times and nothing from this video seems to match the physical space.
Potential (or unsolved) clues:
"Spectacles is like face glasses they is!"
(a) "Ya best mind the gap in yer face!" - Subway reference to England's "mind the gap" at their subway.
(b) "There are 4 in the crew. He's seen 4 docks";
(c) "There are 5 docks at the Port of Cortland"
(d) "But you can't see all them docks at the same time". - I was thinking Mulligan was a Port Authority, because he seems to know more about ports?
(e) the shuriken/throwing star
(f) the Larry King's map in general.
(g) First order of feed backgrounds is orange, orange, yellow. Second order of feed backgrounds is orange, orange, yellow, then blue on bottom. Last order of feed backgrounds is blue on top, then orange, orange, yellow, yellow. - Are these cues to take the subway, because as someone pointed out, these shades are almost exactly those of the subway seats?
(h) The news ticker! It says "IF YOU SPENT THIS WHOLE EPISODE READING THE TICKER, THE BAD NEWS IS YOU MISSED THE CLUES". This might mean there are no clues in the ticker. I think it means there are clues in the ticker and in the video, but the ticker clues apply to other videos, like how it tells us the gorilla is not a clue.
Do the Arthurian legend references fit anywhere else?
EPISODE FOUR COMES AFTER SIX, ACCORDING TO CROTHERS' MISSING LIMBS!
Episode Five
Are the cards significant? What do we think?
1. - The Captain wins a side hand against Crothers with a J Q against 5 6
2. - Black Tom's hand is J J
3. - Crothers' hand is K 8
4. - Mulligan's hand is A H
5. - The Captain's hand is 3 4 5
6. - The flop is Q K 6
7. - Black Tom changes his hand to Q Q
8. - The turn card is H
9. "Lady luck has hit the end of the line, she's gone back the other way!" - We hit the end of the line and turn around?
10. - The river card is 8, which doesn't help anyone
11. - The stone disk is revealed and points to north-northwest
Episode Six
"The telephone number listed as the customer service number on the GENERAL ANESTHETIC TOOTH CLEANING WORKOUT KIT advertisement is an actual phone number. (307-275-1033)
If you call the telephone number you will be treated to the following recording:
A cheery tune plays and the voice of the Captain is heard.
Captain: You've reached the pirate lottery hotline! This week's winning numbers be twenty, seventeen, sixteen, fourteen, twenty-one, and twelve. On the treasure ball be eight. If you've got the lottery ticket what has all these numbers, tear up the lot. T'aint what they're for! Har har har har har har har har har har!"
20, 17, 16, 14, 21, 12, 8
Episode Four
Note: since all of these clues are unsolved I will just list them in order.
1. Japanese characters reversed horizontally that mean "northern division"
2. Sometimes to follow the way, you must avoid the way you've known (spoken backwards)
3. CLUE 41
4. CLUE 42
5. CLUE 28 (FURLONGS)
6. CLUE 43
Episode Seven:
The gorilla in the cabin is not a clue, according to the news ticker from episode three: "THERE'S EVEN AN HOMAGE TO AN HOMAGE, AND THERE IS A GORILLA. NOT THAT HE IS AN HOMAGE TO ANYTHING, BUT HE ISN'T A CLUE EITHER. GORILLAS JUST MAKE EVERYTHING A LITTLE BIT BETTER"
Episode Eight:
Satan is Santa to Mulligan. - Anagram?
T->N
A->T
N->A
References to beer, sweets, and sugar.
“Look for the flying birdie and follow his path. And start from the ship, that’s important too. Oh, but away from his nest. A birdie....Oh, now I is a bird! That’s irony, that is!”
"We should have been listening to him from the very beginning"
"Tutty were the treasure I were truly missing. In a way, it turns out the treasure was with us the whole..."
but anyways...when I heard north by northwest I immediately thought of the alfred hitchcock movie. Perhaps if you watch it there may be a clue there?
