Belfry's excellent intro has some thematic threads that it might be interesting to try and follow through, I'll have a crack when it comes to 1961.
One somewhat more prosaic omission was the world of sport (in general, not Dickie Davies et al who didn't start up to for another 5 years). So a few random facts from 1960...
Two countries that no longer exist fought out the first Euros final in Paris.
GB took home a paltry two Golds from the Rome Olympics but managed to get embroiled in controversy by seemingly fielding two intersex athletes.
It's possible Belfry chose to draw a veil over sport as it wasn't a great year for City, we managed to get beat 1 - 5 at home by Div 3(?) Southampton in the 3rd round of the FA Cup and despite some big name players managed 16th in the league.
How to get a song out of those? From the 1960 film Can Can, Lev Yashin and co probably felt this way...
I Love Paris - Frank Sinatra