The small fox-like creature on Yagami's bag is apparently a character from Takahashi's "Lum" ("Urusei Yatsura") series. (Thanks to "Murasaki" for this info.)
First appearance of Yagami's parents.
This episode must take place only a few days after the previous one, that is, still early in January.
This episode takes place immediately after the previous one (evening of the same day).
This episode begins 3 days after the previous one.
Apparently, the theme of a girl of Yagami's age working to support the man she loves was a rather common one in the "shojo manga" (girl's comics) of the late 70's and early 80's, and Yagami must have been reading some of these. (Thanks again to Murasaki for this info.)
In spite of the date of publication, the date given in the story is "the end of January" (first panel of first page), which gives an idea of how long Yagami has been staying at Maison Ikkoku.
There is a bizarre error at the end of this episode (in the comic-book version, at least): on the last panel of the last page it says "On the spring in the year of Maison Ikkoku..." which is meaningless as far as I can tell. The original says, instead: "March, 1985"