TNG didn't really take off until after Gene died, if you notice that's when we started to get more character based episodes, rather than the plots being focused on solving the problem of the day.
Several of the actors had mentioned that they had approached gene about expanding their characters but he was pretty set on having the "problem of the day" format.
I believe this happened around season three which would have been around the time Gene passed. That's really when the series took off and the characters became more relatable and endearing to viewers, where Picard became less rigid, Riker became less awkward, and actually earned more respect after his handling of Wolf 359 etc...
Data became more, well, human...Worf showed other emotions and became a vehicle for comedy, Geordi became the nerd/geek that was so beloved and endearing...Counselor Cleavage (Troi) got less melodramatic, Crusher got to explore ethics and principle far more...
So yeah seasons one and two, when going back, you definitely see a paradigm shift from season three onwards.