These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
And, apparently, if The Other Wiki can be trusted, not-quite-licensed (either from the original artists, or, quite frankly, by the Soviet authorities) music from Western artists such as Herb Alpert and his Tijuana Brass that came from the production staff's private collections.
Most obvious is when elegantly dressed Wolf comes over to Hare's house with apparently very friendly intentions and a bouquet of roses, and proceeds to open a bottle of cider (rare in the Soviet Union at that time). The fact that Hare is implied to be male but is voiced by an actress known for her extremely high-pitched voice certainly doesn't help.
This is somewhat of a case of Values Dissonance: to a Russian viewer, this would just be Wolf sucking up to Hare, not outright courting him. Then again, one must wonder for what purpose Wolf has to suck up to him...
What also doesn't help are the lyrics to the songs, most of which about love. Episode 7, for example.
In Episode 2, the Wolf and Hare dance the tango, with the Wolf carrying a rose in his teeth. In Episode 19, the Wolf dresses up as a woman to sneak up on the Hare.
Hilarious in Hindsight: In episode 4, the Wolf steals a camera and begins to take "selfies◊" (close-up photos of himself), each with exaggerated poses and expressions like how they are done in the 2010's.
Viewer Gender Confusion: A Zig-Zagging Trope for Hare. It's an Averted Trope in homeland Russia, because the hare in question is called/named just the Hare, and the Russian word for "hare" ("Zayats") is masculine by default, implying that the Hare is indeed a boy. Don't ask. He is also wearing shorts. Unfortunately, played straight for Hare for those in other countries who caught the export version as Hare's somewhat high-pitched voice was imitated by the English VA, his engagement in feminine activities were left untouched, and Hare's gender was never really brought up- many didn't really noticed the shorts or assumed him to be a tomboy.
The trope is played straight with a lot of other anthropomorphic animals appearing in the series, whose genders are determined mostly through the pants vs. skirt method.
Unintentionally Sympathetic: The Wolf seems like a vaguely sympathetic awkward teenager (or, thanks to his deep chain-smoking voice, a 40-something blue collar down on his luck), whereas the Hare usually comes off as a bratty little kid.
The Wolf is pretty much the Villain Protagonist. The Hare is there mostly to give the Wolf something to chase. The Wolf can act without the Hare and still carry the show on his own, while the Hare, with his "perfect boy" persona, would get insufferable very quickly if alone.
YMMV, as Wolf acts quite visibly like a total Jerkass.
Uh, it's the whole point. Take an annoyingly bland Designated Hero so full of propriety that even the air around him Tastes Like Diabetes, let a hilarious hooligan practice apparently motiveless aggression while fumbling anything more than Poke the Poodle, and you get a good pair for slapstick. Because the viewer really roots for neither Hare nor Wolf — they both deserve what they get. Much the same recipe was used in Leopold.
Unresolved Sexual Tension: as weird and squick-y as that implication is in a children's show, the Hare constantly bails the wolf out, despite the implication that they are mortal enemies, whilst at the same time the Wolf is singularly targeting the Hare, going as far as to ignore all other rabbits he comes across which would imply that it's not his appetite he might be looking to satisfy with the poor bunny.