Personally, I did not dislike Sakura part one. I didn't dislike Naruto part one either. Their most outstanding flaws (Sakura being a fangirl, Naruto being the idiot-rival) was already starting to tone down by the first arc, and they were so obviously not meant to be taken seriously that while I could see being annoyed by it, and I agree that it certainly could be, I didn't take it as annoying. During the time they were at their worst I was more interested in the plot, the story, and was trying to judge it as a whole. Funny, the two most "annoying" characters part one became my favourite by far. Naruto and Sakura are my favourite characters and they were even when I was a SasuSaku fan--though even then I did pick up the romantic and friendly moments of NaruSaku.
Here is where I see the double standard in first impression alone. Why do we forget that Naruto was hung up over Sasuke too? It wasn't romantically--it was in the rival sense, but he was adamant on beating Sasuke and he was trying hard to overcome it, but failing. I acknowledge that people may find being obsessed about trying to best somebody is better than being in-love-obsessed; after all, we have negative words like fangirl and stalker, but what do we have for the obvious underdog trying to beat somebody? Idiot, loser, dead-last maybe, but they're not really specific like fangirl and stalker are. They were both trying too hard, and they still continued to have a very Sasuke-oriented focus even up until now but I would argue that for the beginning of part 2, it was way more emphasized as Naruto's kind of "hopeless" pursuit than Sakura's. In fact, Sakura had a much more team-7 and "help them both" attitude rather than it just being all about Sasuke-Sasuke-Sasuke, and this wasn't an overnight thing. She had implied it late part 2, and we've seen her worry about the rivalry between Sasuke and Naruto on the rooftop, and when Naruto was trying hard during the chuunin exams--wanting to go as far as failing the team so that Naruto could keep his dream of becoming Hokage... It wasn't outright stated, but you know that that would be disqualifying Sasuke too--you know, the person she's all fangirling over?
I understand the first-impression issue very well--in fact, in social psychology we talk about the power of impressions. This is an every day life thing we all suffer from, and an example would be that sub-consciously depending on how someone just describes another person to you, whether it is positive or negative, before you even meet them you have a bias and it's not easily shaken off because EVERYTHING that that person does you use another bias called the confirmation bias to support that impression/belief about the person and disregard the good. It may be why Hinata seems unable to do wrong--we do get a better first impression of her, as minor as it is-- and Sakura can do no right by some people in the fandom. Yet, there is a double-standard... Naruto does not get this amount of pressure from the fandom even though he didn't have the best start.
I went to a panel this year at Anime North about writing strong female characters. The panelists, some were published authors, and we had one professor of anthropology, explained that female characters all seem to carry this burden about being female, and therefore more scrutinized. A male character can get away with doing more than a female can. This is not just a sex issue, but it's the same when you're a minority character, or a homosexual character. For whatever reason, and I think it's just ridiculous, when you're female you have to be portrayed just right. If she is physically weak, typically female. If she has romantic issues, typically female. If she is emotional, typically female. There is a pressure to make her more masculine, but somehow still portray her as a realistic female. Suddenly, female characters have to be role models and have to be acceptable, or she'll be praised for being in a role that is typically a male dominated role. If she's the ace, if she's the tough one, if she's made of ice and is only focused on the quest or whatever it may be.
I've never minded feminine characters male or female. So, if I can accept a guy who is just a side character to provide support, I can accept it from a female too. It does get annoying when it seems that a role is being shoe-horned, like only males seem to be great fighters and girls tend to be healers/support, but that was annoying in Sailor Moon where it was females but granted there weren't many male characters at all. We had Tuxedo Mask... and well the villains were male but not the Big Bad. In Naruto, we have a number of female characters and while I'm not as hung over about it that Sakura isn't a super-awesome fighter because, my gosh, that's all anyone seems to be in this fandom lately, I can see the frustrations. I think Sakura is a true character, with complex relationships, feelings, and growth, that doesn't rely on special blood-types, jutsus, or special pasts with special families that have special talents. Sakura was given no handout, except her intelligence, but in a manga of special fighting intelligence only counts if you're Shikamaru who has a super-special brain that can think of 200 different scenarios in a second. I'm more disappointed that Kishimoto doesn't show more "normal" skills of the ninja world being used effectively. Where above-average, not super, intelligence and techniques, not clan-abilities, can be useful in battle. This is where Sakura gets her "useless" title--she's not super-special-awesome. Tenten gets called it too, but let's face it, she's not important enough and is hardly a character herself to get too much scrutiny.
^^^^^That paragraph up there is a little bit off-topic, but I think it is a factor in why Sakura gets more scrutiny. Even if Naruto can be annoying, Sasuke-obsessed, angry, and flawed, he is a good fighter and the plot is heavily about him. Sakura can be annoying, Sasuke-obsessed, angry, and flawed, but she can't match up to Naruto's level of power. I think being a healer is a great thing, I think the fact that she is able to fight off a genjutsu is wonderful--I wish more was being done with it--and she does pack a punch and she's not hopelessly lost on a battlefield, but she's not the one throwing volleys of powerful jutsus and so she can't match up to the big fighters and so that's reduced to incompetence. We haven't seen her fight against the side characters with "lesser" abilities (but all save for Tenten and Lee have some clan affinity) so we don't know if she can hold her own against them, and from what I've seen is the popular opinion is that clan ability trumps regular ability. Training with the hokage apparently doesn't give her an edge and let's face it, we don't see enough of her fighting. She did fight against Sasori, but because she had help some say it didn't count... but we're not criticizing that Shikamaru had help, and from more people might I add? Sakura had Chiyo, who is an old woman. Shikamaru's teammates were those two guys, Ino, Chouji, Asuma, and even Kakashi and Naruto stepped in to help defeat Kakuzu. I'm not undermining his achievements, it's just his often are not whereas Sakura's are.
I don't think either Naruto or Sakura are perfect characters, and I mean that they are handled well from a literary point of view. They both have moments that seem inconsistent, strange, awkward, and even unlikeable. All the same, my perspective is they are both great, and my bias is I tend to look upon both favourably rather than unfavourably, but I do think that sometimes even I turn a harsher eye to Sakura. I think it's because she's just so unusually normal and so I want her to have as many good moments as Naruto does, but in this manga good moments are fighting moments. He's won and fought a lot of battles. Sakura's good moments usually aren't so obvious or highlighted, and while her bad moments are just as small sometimes, for some reason they stick out more. I can more easily recall the times Sakura was pushed down, or crying, or saying something mean-spirited than Naruto did, but I know he had those moments too. It's easier to recall Naruto's shining moments as well, but I remind myself, he has far more screen-time and he's the main character and unless it's about Sasuke, everything comes back to him story-wise.
It an unfortunate double standard and I think one part she's female, one part she's not a stellar unique fighter in a shonen manga where that's a big thing, and that she has a mixed bag of rather subtle moments that don't easily stand out, and depending on the impression that one gets early on good or bad may stick out more.
I thought I was the only one who felt that way sometimes.
When Sakura was weak in part one, all the fans hated on her for it and called her a disgrace to females. I was like, okay, the average fan prefers a girl who can kick ass over one who doesn't really pull her weight. You could imagine my shock when the Sasori fight came along and people were hating on Sakura for being a Mary-Sue... DAFUQ? I was like, "This is what you wanted, you guys!!??"
It looks like, when you're weak, you're a disgrace to females, and when you're strong, you're a Mary-Sue. Shikamaru did pretty well against Hidan, and I don't remember anybody criticizing him as a Gary-Stu for being strong. And if fans did, definitely not as much as how much fans did for Sakura.
Anyways, the strength of a character doesn't really matter to me. If it did, Sakura wouldn't be my favorite character because I would be fangirling over like Madara or something. Honestly, I don't think strength is the be all end all for most people, or many characters would not have any fans at all.