Pretty Soldier Sailor Moon S Gekijouban
Pretty Soldier Sailor Moon S: The Movie

This movie is based off the Sailor Moon short story "The Lover of Princess Kaguya"
written by Naoko Takeuchi. 

3:14 Usagi's food

Usag is is eating "taiyaki" a type of cake made from usually pancake batter in a 
fish-shaped mold and filled with red bean paste, though there are variations such
as waffle batter and custard and chocolate fillings.

3:26 Television screen reads:

Miss Himeko Nayotake

3:37 Usagi's food

Usagi is now eating "takoyaki", a battered snack with octopus on the inside.

3:54 Entrance Exams

In Japan, paths of education can be quite restricted and so even between junior
and senior high schools, there are exams to ensure the high school of their choice,
these are essential to many Japanese students.

7:06 Usagi's Luna images

These just read "Klutz, Scatterbrain and Crybaby" respectively.

7:25 Sign reads:

Space Pioneer Enterprises - Space Observatory

8:33 Princess Snow Kaguya

The Tale of the Bamboo Cutter, a Japanese folktale includes the character Princess
Kaguya who comes from the Moon, hence Kakeru making the connection.

10:13 Marshall

She's referring to Marshall Space Flight Center located in Alabama, USA.

10:53 Kuro and Tama

These are among the classic cat names in Japan.

10:55 Mike

The reason why Kakeru dismisses "Mike" is because "Mike" means tortoise-shell 
pattern and is therefore usually only given to Calico cats.

11:01 Tsuki

Tsuki is the Japanese word for Moon.

11:24 Usagi though bubble reads:

Elegant

11:28 Sugar stars

This is konpeito (from the Portugese confeito), a popular sugar candy in Japan,
they come in multiple colours but they usually are not flavoured. They are referred
to as "sugar stars" in the translation to make the connection between the konpeito 
and the space theme of the movie closer.

21:19 Blimp reads:

New Year Holiday Huge Bazaar

25:14 Burning leaves

They're roasting sweet potatoes under the leaves that they've raked and have
burned, a popular cold weather activity.

29:42 Nippon

Nippon is the Japanese for Japan

55:20 I can't stay by your side forever

It is important to note here than though there are variations on the Tale of the
Bamboo Cutter, Princess Kaguya never stays and Earth and always leaves for the Moon
at the end of the story. This is represented here between Luna and Kakeru.