Snivy is my favorite of Ash's Unova captures, for its maturity (not a very sophisticated reason, I know). It's nice to see the way it considers Ash, liking him for his protectiveness of Pikachu but also not so sure that it wants to be captured. That's really all there is to it; it's a very simple plot that's expanded to fill out the screen time.
There are 2 scenes that really stuck with me, one being the glare Ash gave Iris when she criticized him for not knowing how Attract works (I was about to roll my eyes, but Ash had the better reaction). The second, and much more meaningful one to me, was when Snivy escaped from TR and laid down on the rocks deep in thought, not really taking too much notice of Pidove circling overhead. It's a somewhat sinister scene, knowing that Pidove is going to bring Ash to try and catch Snivy again.
Ash almost drowning in the mud-river(whatever it's called) was pretty shocking, since this didn't seem that dangerous to begin with. We've seen Ash just across chasms rather than take a bridge across and do other crazy things, so it's startling to see him almost done in by something like this.
One serious thing about this episode, though, is the way Ash relentlessly pursues Snivy, even though it doesn't want to be caught at the beginning. It's not the right thing to do, to force someone to like you when it's really not there at first. Snivy is shown to be a very mature pokemon, so the argument that it's just a pokemon doesn't really work here. I sincerely think Ash should have respected Snivy's wishes after it doesn't willingly want to be caught, and then Ash fails the first time to catch it.