I would have to say that by far, the most important details when it comes to alignment in yoga practice, are the yamas and niyamas. Hands down. Without a firm foundation in the yamas and niyamas, it's not going to matter if your leg is straight in Triangle or your sitz bones are even in Dandasana. Granted, you start where you are and if where you are is in a pose it may lead you back to your life and to the yamas and niyamas, however, our culture (and probably not just ours) loves to leave the yamas and niyamas behind like they're some archaic remnant of earlier teachings. Not so.
The yamas and niyamas are so current and so powerful that it's no wonder people shy away from them. When people start practising non-harming and telling the truth and simple things like that, their lives change. And nobody wants to go to a yoga class and have to start changing their lives. We don't want to start being considerate of others or stop stealing office supplies from work. Who wants to be responsible for their own pain and peace of mind? Nobody! We want the government to take care of it or other people or start a new business or find the right partner, maybe even in the next yoga class we go to.
If your yoga teacher doesn't know what the yamas and niyamas are or hasn't had a practice of them that they can tell you about, I'd say you might be in a stretching class. I'm just saying. Because lengthening your hamstrings and relaxing your shoulders really isn't going to make a bit of difference without them.
After being a part of the teacher training for years now, I can confidently say that the most transformational piece that people get is what they see about themselves through the practice of the yamas and niyamas. That's the part of yoga that will blow you away and make you so grateful you were led to the practice in the first place.