Buffy/Angel is the worst example of this. Now, I have the disadvantage of despising the relationship and thinking they have no chemistry (though I do like their dynamic as exes, but unfortunately they were not really exes in S3), but: In S2 the schmoopiness was set-up for a beautiful subversion (that was undermined when Angel immediately appeared in S3 credits and returned after only a few episodes). In S3, their relationship went precisely nowhere. It was just killing time until Angel left for his own show. The eventual breakup had been coming the entire season and was supremely anti-climactic. For that matter, it was frequently very confusing as to whether they were actually together or not. Buffy calls it quits in Lover's Walk, and then Amends happens, and then...at some point they're back together. gabrielleabelle's poll takers had different opinions as to when, exactly, this happens. There's a similar issue with Buffy's relationship with Faith, but I'll get to that later.
Enemies raises the possibility of raising questions about Angel's ability to play Angelus so well, but this is quickly transmuted into Buffy's jealousy of Faith. In S2, Willow bluntly points out that both souled and soulless Angel think only of Buffy, an undeniable connection between the two. S3 shoves that rabbit back in the hat of subtext, and it is hinted at but isn't explored, leaving the Buffy/Angel relationship bland.
As for Angel himself: Amends and his attempt to reach out to Faith are apparently intended to prepare him for his own show. However while these events do show us Angel's perspective in a way we didn't see before (with the possible exception of the Becoming flashbacks), they don't really advance Angel's character or show us anything new. We know Angel feels guilty and tortured by his past. We know he's seeking redemption. It doesn't change anything.
As for Buffy: There's a reason Anne is one of my favorite (if not my absolute favorite) episodes of the season. She actually has character development. But after coming back, Buffy's mostly in a holding pattern, too. She's mostly dealing with the balance of being the slayer and being a normal girl, which has been her story since S1. Her relationship with Faith is the most dynamic part of her arc, but unfortunately the way that ends demonstrates the pointlessness of S3. Buffy tries to kill Faith, stabs Faith, puts her in a coma for months...and it has no effect on Buffy whatsoever. Buffy's decision to kill Faith is barely even mentioned again. Buffy isn't wanted by the police. No one in her circle seems to care. And any guilt she feels is a non-issue after the S3 finale. Any feelings she has about it all at all seem to be a non-issue after the S3 finale.
In the meantime, Xander and Cordelia break up not for any reason organic to their relationship, but because Xander randomly cheats on her with Willow. Cordelia spends the rest of the season in the awkward position of being a regular who is estranged from the gang. Xander for his part has the Zeppo, a revelation of confidence that doesn't really stick (gabrielleabelle's pollsters point out that he's back to sniping at Cordy the very next episode), and his relationship with Faith. It's telling that both Buffy and Xander's arcs are at their most dynamic when it involves Faith. I will get to Faith.
But in terms of Faith/Xander: Even after she sexually assaults him and tries to strangle him (leaving noticeable bruises on his neck, something many fans forget), the one night stand becomes a joke (including a particularly insensitive crack from Faith herself in S7). In contrast to Spike and Buffy in later seasons, the effects of Faith's assault on Xander are not explored.
As for Willow: In some ways she has the best arc of the core four, as she gradually develops into someone more confident, both socially and magically. The Willow/Xander affair is nothing more than a hiccup in her relationship with Oz, and the sex in Graduation Day isn't particular interesting except in the context of Willow seeing herself as becoming more grownup and more cool. Doppelgängland is a key episode for Willow and her changing self. During my first watch of S3 Willow's arc was too subtle and had too little pay-off, but the pay-off comes in the later seasons.
There are, of course, some arcs this season: Giles and Wesley and the council are important, although the obvious badness of the council make Buffy's decision to quit feel too delayed - and her reason for finally quitting, a reversion to early S2's "nobody messes with my boyfriend" is unsatisfying. The Mayor is one of those villains who I feel like I ought to like more than I do.
Then there is Faith.
Faith is undoubtedly one of the best things about S3, and few characters are more dynamic. However, much as I love Faith, there's a reason I find her redemption arc considerably more compelling than her fall to darkness. Faith's fall is fragmented and confusing. Before she goes dark, her relationship with Buffy is even more inconsistent than Buffy/Angel, with them going from not talking or making eye contact (beginning of Amends) to best buddies with Faith influencing Buffy to engage in illegal behavior with only a scene or two to bridge the gap. Faith's fall from grace begins when she accidentally kills a human being, an echo of Buffy's apparent manslaughter in Ted. But while Buffy, our heroine, is given an out (it was a robot!) secondary character Faith is not. Yeah, that's not a cop-out. Faith is, of course, 100% responsible for her subsequent turn to the dark - but her lack of connection to the Scooby gang means that no one seems to care too much, outside of key episodes like Consequences and Enemies. Faith's status as a reoccurring character and not a regular hurts her storyline and her connection to the Scoobies.
In contrast to S3, one of the things I love about S4 is that SO MUCH changes. All three of the younger core Scoobies get involved in new relationships, and in contrast to the Xander/Cordy break-up, Willow and Oz's break-up (and subsequent decision not to get back together in New Moon Rising) is organic to their relationship. Even Giles has a sexual partner we haven't met before. The Scoobies start college, completely changing the game. Spike gets a chip, another game changer, while Faith starts her redemption arc.