The TOS episode "Requiem for Methuselah" has got to be one of the best examples of giving the designated "smart" character random knowledge for plot purposes. Okay, Spock can play the piano--that's fine. He already plays the Vulcan lute, and it's not uncommon for musically-inclined people to play a second instrument.
But he not only has seen samples of Brahms's handwriting in a museum or electronic archive or wherever, but is good enough at forensic handwriting analysis that he can recognize it, not just as generally "old-style handwriting that kind of looks like that sample of that Brahms score I saw once," but "looks just like Brahms's handwriting, specifically"? And he knows enough about art that he can say that painting doesn't just look kind of stylistically similar, but definitely is an authentic Leonardo da Vinci? Really now.
But you can't really blame the writers of that episode. Just take a look at Spock's skill set, when you look at all the episodes cumulatively:
-Computer programming (super expert)
-Military game/simulation design (Kobayashi Maru test)
-Astrophysics (super expert; can even invent time travel)
-ALL THE SCIENCE
-Three-dimensional chess (Grandmaster status in AOS, possibly in TOS)
-Ka’athyra (second best on Vulcan, or at least second-best of non-professional musicians)
-Forensic handwriting analysis (with bonus knowledge of historical figures’ handwriting)
-Military strategy and tactics
-Management (you just know Kirk leaves most of the paperwork to him, too)
-Warp core repair
-MacGuyvering lasers out of subcutaneous transponders
-Diplomacy (later in life)
-Emotional control (most of the time)
-Xenolinguistics (in AOS, at a level competent to teach advanced students; unknown whether he studied this in TOS timeline as well)
-Intercultural ethics (in AOS; competent to teach)
*PROBABLY ADDITIONAL MAJOR SKILLS I'M FORGETTING BECAUSE DUDE IS RIDICULOUS
And he can quote poetry and Sherlock Holmes. And is sexy and multiple female characters want to get illogical with him. Oh, and he's also longer-lived, needs less sleep, and is just generally harder, faster, better, stronger.
And nobody complains how unrealistic this is.
Not that I'm saying anyone should! Spock is awesome, even if he is also a jerk sometimes because the writers couldn't quite envision a future without lines like "I have never understood the female capacity to avoid a direct answer to any question." I just think it's... interesting that some characters can get away with so much, while other characters get slammed if they so much as play one instrument while being sexy scientist military commanders.
This also is why I don't accuse characters of being Sues just for being ridiculously talented; sometimes, that works! To be Sues, to me, they have to warp the fabric of their fictional universes so badly that my suspension of disbelief snaps and and flings me off the metaphorical bridge.
But mostly, I just find that list of skills hilarious and had to share.