I rewatched TNG, Voyager and Deep Space Nine over the last 12 months or so. The first season of TNG isn't as bad as I remember it, and some episodes of Season 2 are far worse. I suppose the best thing about Season One was John de Lancie's Q - an absolute delight to watch in any of his storylines.
I too used to think that Tasha's death was a real let down, but after reconsidering, it's probably one of the only realistic portrayals of death for a 'main' character. Usually they will go out in a blaze of glory, sacrificing themselves for some noble cause. But in the Star Trek universe, security officers die all the time, often unexpectedly and in the line of duty carrying out their job. Tasha's death kind of brought that home, and made her seem even more 'human' a character. And the eulogies at the end of the episode were beautifully done.
But yeah, if it hadn't been Star Trek, it's quite possible that the crew would never have made it to Season two.
Whilst there are loads of shows that start great and gradually go downhill, there are far fewer tv that start off poorly and then get the chance to improve. I suppose the most obvious one is Black Adder, with the first series being entirely different (and much less funny) than the next three.