You'd have an easier time escaping Riker's Island than the dreaded Friend Zone. "But I have this one friend who knew this chick for 5 years......." Don't want to hear it. Move on, if you were a sexual option it would have happened by now. Every woman has loads of "guy friends" that think they are one drunken night out away from making it happen. They aren't.
Generally, everyone first reads "The Game", then Mystery's book, then blogs and online forums. Many people take bootcamps which are generally 3 days of lecture and 2 nights in bars approaching women. I took 2 bootcamps with the top companies. One was a regular comprehensive bootcamp, one was a specialized one. I also attended 3-4 special seminars by instructors who had good reputations. At the beginning it was a little like learning martial arts. Some people advocated jiu-jitsu, some Krav Maga, and interested students wanted to know what worked best. Over time all the theories and strategies narrowed down to a more or less to a single consensus much in the way the various martial arts eventually turned into the Mixed Martial Arts you see practiced in UFC.
12 beers. No, I'm kidding.
One word: Volume. The more you do it, the less any one approach means to you. If you work up the nerve all night to talk to one girl and it doesn't go well you'll feel it a lot more than you would if she was one of 10 you talked to that night. Over time you'll also develop a thicker skin and a realization of how much of a woman's decision to say "yes" is influenced by a multitude of factors you have nothing to do with.
Although I'd love to avoid the cop-out answer I can't.... there are all kinds. In my bootcamp there was a 23-year-old millionaire who had been with 300 women, a guy nearing his 50s, a successful Asian director, and a bunch of computer programmers. I'd say about 20% of my clients are, well...virgins. But there are plenty of regular dudes...investment bankers, lawyers, etc who just need the nudge.
If you have "zero game" as you say, it's unlikely to improve just because you set foot in an establishment that serves coffee instead of alcohol. Women don't change species just because they are in a club. Work on the game part first...are you anxious? Dull? Overly deferential? Address whatever it is head on. Once you've managed that, then you can start worrying about the types of venues that will enable you to meet the most compatible women.
I will say that Bed Bath and Beyond is highly underrated (I'm serious)
Bragging. Or worse, humblebragging. It's utterly transparent. I'm sure you are proud of the Law & Order-worthy case you've laid out of why she should like you but that's not really how it works. As far as correcting it, pretty simple. Knock it off.
But really "mistakes" or any thing revolving around technique takes a big backseat to just overcoming various fears and insecurities which, unfortunately, take more time and effort to "correct."
All of them. That's not to say all women are the same. Women respond to power and status, for example. But power and status for a 21 year old club girl means something different that it does to a 28 year old corporate attorney. The knock on the "techniques" is that they only work on insecure women but while there's a grain of truth in that, being charming or having good game is something virtually all women recognize and respond to.