I should probably hesitate to say this is the exact point at which they became interesting, as a lot of people obviously like their older stuff too, and I'm not 100% familiar with the exact chronology of their releases, but this record must be pretty close to the transition point.
Although "Lennon and McCartney" appear on the credits to songs written by only one of them, this was a genuine co-composition. According to Wikipedia, this is McCartney wrote most of it before enlisting Lennon to help finish it off, but Macca credits George Harrison with the idea to waltz-time the end of the "Life is very short" section (where it goes "and fighting my friend").
This is when the song-writing became a little more sophisticated and, for me, way more interesting. (I'll do a piece on Happiness is a Warm Gun at some point - that's crazily all over the place - in a good way).