Warning Contains some spoilers.
These things frustrate me about chobits
1) Sometimes Chi does something incorrectly or embarassing, but Hideki refuses to tell her that it's wrong and instead tells her she's ok. She's built to learn how to do things. Telling her the incorrect thing is ok will mess up her learning program.
2) Why are all computers stored in people shaped containers?
3) Why are there legal limits to how fast the internet is?
4) Why does Hideki freely trade porn magazines with his boss, yet remains afraid to enter the underwear store.

It's written by Clamp... Details are not their strong points.

Suspension of disbelief. I agree though, there are a lot plot holes (in almost every show) that frustrate me. I just try and ignore them and enjoy the story that's being told.

It's not that I don't enjoy Chobits (For me, the cuteness carried the show long enough for me to start to care about the characters), but the push for Chi and Hideki 's 'romance' seemed very forced. I seen other anime which had much more natural relationship growth.
1) It starts out with hideki having 4 potential love interests:
a) The manager, but that relationship never rises above being, mainly because
b) The teacher, but that relationship never becomes anything, because
c) Yumi, who is highly flirtatious and seems very interested in hideki
d) Chi, who doesn't really have much personality to speak about. It really seems like she's four, which makes her romance with hideki creepier in hindsight.
2) Having the other three love interests be essentially fake love interests makes for poor drama. It seems like all obstacles to their relationship must be bulldozed away.
3) It's hard to suspend disbelief when a story breaks it's own rules

Harem romances are not typically made to be built on sound plot device. Welcome to anime, it's nice to see some new faces once in a while.

Welcome to the realm of anime ^_^

Relax dude.. seems like you're putting more thought into it than necessary.. way too much thought. It's like you're questioning the very essence of anime, none make logical real world sense. Some are just more descriptive than others about how things work and stuff, so you aren't going to get your answers otherwise.

the thing I find frustrating about chobits is it wasn't the manga.

well, first off, like a lot of CLAMP's earlier works adapted into anime, the manga itself was not that long, I think it was 8 volumes, and the chapters were pretty short. And, like Cardcaptor Sakura, a lot of plot elements were contrivances to allow them to draw the principal female character in as many cute outfits as possible. The exploration of the theme in the manga is, quite frankly, pretty superficial, and most of the characters kinda spontaneously told Hideki all about the pros and cons of persocom love. In a lot of ways, I think the anime is better paced, since it spends a little longer on certain things.

Anyway, the point of that is, a lot of the little things you mentioned in the OP, like Hideki's embarrassment and his reactions to Chi, are because the manga's chapter lengths are pretty short, and (esp. earlier on), it tended to follow a basic formula. Try not to think to hard about the details, since most of those scenes are just vehicles for ecchi jokes to appeal to the audience.

As to the question about persocoms, I think this question is kinda asking why everyone in the Pokemon anime is so into pokemon all the time. Or why everyone in JoJo's Bizarre Adventure has to fight using stands. There are probably still conventional desktop computers and whatnot around in the Chobits world, but its really not the point of the show, so they don't talk about it.

Most of your other frustrations are related to common tropes in shounen romance in general. In shounen romance, relationships never really advance past the first stage for the male protaganist, because: a) romances need as many obstacles as possible to success, both to add dramatic tension and to make the declaration of love more..."pure", I guess?; and b) it allows them to put the main character in various ecchi situations and still not be "unfaithful" to the female protaganist. This is also why these shows mostly have donkan main characters.

Anyway, the TL;DR version: its anime, they don't explain things unless they really have to, and mostly, the plot holes are there because they really wanted a certain scene in there and didn't feel like explaining it.

It isnt a story that was meant to be all details like death note or something, it was made to be cute, funny, and have its serious points at times. I think it does well over all what it meant to do.