1999 Summer – The Legend of Kaguya Island (Revised Edition) - Summer Vacation! The Jewel Expedition Party
1999 Summer - Kaguya Shima Densetsu (Kaiteiban) - Natsuyasumi! Houseki Tankentai

02:47 Artuqa

Possibly a reference to the Artuqid Dynasty, a Turkish Dynasty
which may be connected by Mount Ararat and the Story of Noah,
deluge myths feature strongly in the Kaguya Musicals.
In the original Kaguya musical, this is called Artiqa, but in this
musical and both Shin Kaguya musicals, it is called Artuqa

7:52 Leah Ruby 

Leah speaks in a rather thick Osakan accent, this is somewhat important 
but difficult to translate effectively so her Japanese has been translated as regular English
Despite this it should be clear her accent is noticeably different.

10:57 Akadama 

Akadama can refer to jasper, a red jewel, it literally means “red ball”, Rubies come to mind...

13:57 Bananas do not count as snacks

This is an old hackneyed Japanese joke
In elementary schools students used to not be able to buy more snacks 
than a certain amount of yen. 
Children used to try and get around this, such as making their own snacks, 
The most notable example is students asking if bananas count as snacks. 
Leah Ruby is acting as the teacher and Usagi as the schoolgirl. 
Leah Ruby has pre-empted Usagi’s question and Usagi goes on to ask about octopus dumplings 
instead which Leah Ruby has incorrectly categorized as fish.

17:50 Puns are rampant across Asian comedy, SeraMyu is no exception. 
These words are all similar in Japanese. 
Nautical mile = kairi, 
Welcome home = okaeri, 
Turning a somersault = dengurigaeri
Staying out all night and coming home in the morning = asagaeri

19:56 This song is usually just about the turtles, Chibiusa's just added "baka" into it.
“Oyabaka” (here translated as “stupid parent” usually refers to overly fond parents 
but Chibiusa has broken down the meaning.

21:10 Hiragana

Hiragana is the most basic of the Japanese writing systems. 
Being able to write in only hiragana is nothing to be proud of.

20:12 You’re straying halfway through again!

Chibiusa is slurring her words and speaking improperly and lazily
This is common in some children, but Chibiusa should have grown out of it by now

21:40 Frogs are jumping

A well-known tongue twister.

30:37 Ya saw me!

Leah Ruby said “I saw you” in an Osakan accent and apparently the suddenness of it all 
frightened Mamoru, Leah then corrects herself to regular Japanese.

31:29 The Crane's Return of Favour

Leah's getting mixed up, she was trying to tell her own variant of The Tale of the Bamboo Cutter
at some point she started telling The Crane's Return of Favour. Both at Japanese folk tales

31:13 Baldness Return of Favour

A pun on "tsuru no ongaeshi" (The Crane's Return of Favour) 
with "tsurutsuru no ongaeshi" (Baldness Return of Favour)

41:30 Cook

Cook speaks with a rather thick Osakan accent

54:56 Peperoncino

Loof Merrow made a mistake, Peperochino is an Italian word.

59:40 Comets & Contagions

Sounds very much like they're discussing the theories of Sir Fred Doyle.

1:00:25 Chibiusa no Hanran

Some lines in this song as well as parts of the melody
are callbacks to Chibiusa's original song "Matamata Chibiusa Desu"
to help show Chibiusa's transition into a rebellious young girl.

1:02:46 Shake hands!

Hotaru is speaking in the way that you would talk to a dog.

1:17:30 Papparanpappa

In case it's not clear, these are soundeffects for fanfare.
We can use very similar phrase in English.

1:22:20 Cakes Afternoon Tea

Fan of the anime may pick up that Chibiusa actually said "sanji no keeki"
(Three o'clock Cake), Three o'clock is considered snack time in Japan to
many people, since it's halfway between two meals, we do not really have
the same connotations in English however... 

1:29:21 Yake

Another pun scene, burning = yakeru, sunset = yuukyake

1:29:31 Seeramuun

Pierced = tsukisaseta, “tsuki” also means Moon. 
Niggling = serasera, stuffy = munmun
Sailor Moon = seeraamuun