This is actually a tough question to answer for me. Culture shock in Taiwan has been pretty minimal for me compared to other places where I have lived (Japan and Korea). But I'll begin with a few things that I had problems with initially.
Obviously, if you arrive in Taiwan as a Westerner with zero ability in Mandarin Chinese, then you will inevitably experience a little bit of alienation just by being on the outside of basic conversations between Taiwanese people or your foreign friends who are more capable in the language. I definitely felt that way the first year that I was here. And it's pretty much unavoidable until you get the basics of the language down (which will happen faster than you think as long as you are willing to put yourself out there and talk to people).
Beyond that, the food and general dietary customs can present some cultural difficulties if it's your first time abroad. First, people tend to eat family style, even in public with friends and acquaintances, so lots of chopsticks will be grabbing at stuff from the same plates/hot pot. This is only odd at first, and is only a big issue for people that are really OCD about sharing stuff generally. Then of course there are just some dishes that I just can't eat. I'm not big on fish eggs, intestines, or stuff that is heavy on gelatin. A lot of the dessert-type snacks people enjoy here just don't suit my tastes. But that's more to do with personal preference and less about culture shock.
Ok, so having said that...
and having grown up in the US...
I am pretty convinced that Taiwan is one of the easiest, if not the easiest (non-Western country) in the world for Westerners to assimilate to. It might seem hard to believe, but besides the language, I just don't think the cultural barriers are very high for foreigners in Taiwan. That's because Taiwan is kind of a multi-cultural society by nature. People (young people especially) just aren't that rigid in their thinking, and are generally super friendly and welcoming.
The infrastructure here in the larger cities also makes life SUPER convenient. So even if you are a recluse and want to spend all your time in your apartment, Taiwan makes that incredibly easy to do. With cheap food on the go or delivered directly to your door, and 7-11s on every corner to provide for basic necessities, Taiwan just doesn't make life that difficult.
The real "culture shocks" you'll run into will most likely involve relations with your employer or on the dating scene. Or if you marry into a Taiwanese family...But that's a whole different conversation/ level of culture shock than I can (currently) comment on. But those situations will all depend on the individuals involved, and are hardly insurmountable.
I don't want to make it sound like a paradise, because it is still a very hard-working society, and people do keep certain expectations for etiquette and respect for elders/superiors and the like. But in all honesty, if you are looking for a place to "start over" or just spend a few years of your life in a friendly, welcoming, convenient, and beautiful country, I'd recommend Taiwan in a heartbeat. Not saying you won't have culture shock of your own, but I am willing to bet (if you're an American or Canadian, at least) that there will be way less waiting for you in Taiwan than there will be in any other Asian nation.