Re social awareness... surely the earlier you start teaching this to a toddler the better? Once a child can understand language and abstract concepts, they can develop awareness that there are other people living behind the wall. Parents have a responsibility to keep reminding children these people are sleeping etc. Social awareness is learned from parents, but sadly many parents seem to lack even basic social awareness!
I wonder why some parents feel there is no need to consider other people?
For example, Joyful, you mentioned you were not concerned with your neighbours feelings because they were 'wrapped up in their bed' while you had to get up and comfort your screaming child. Isn't this rather a selfish assumption? After all, you decided to have a child, so it's hardly their responsibility. Being sensitive to neighbours feelings (instead focusing solely on your feelings and your child's) is one of the basic requirements of living in a civilised community! You expect your neighbours to be consistently tolerant and empathic, yet this should go both ways. Having a child does not give you the right to be selfish and live in a bubble!
Coola, your description of your toddler is interesting, and I'm sure most people with toddlers can relate to it. Certainly she sounds very like every toddler I have ever met. I think you misunderstand my expectations re my neighbours... of course all children scream, cry, run, disobey, misbehave, have tantrums, have patches of being unsettled... But when this happens EVERY night and wakes neighbours several times EVERY night, it's not enough to say 'she's three' and expect that to be an excuse. Would you seriously expect them to manage on a few hours of fractured sleep each night for a few years, until she grows out of it?! To me, being a 'good enough' parent means not giving up! Most people keep trying to improve their parenting skills. If your neighbours complained they couldn't sleep, would you simply dismiss these complaints as irrelevant and tell them you're not willing to try and improve things?
I will definitely be moving out of this flat before my baby is born. And in light of some people's attitudes towards what is 'acceptable' neighbourly behaviour, I think I will be looking exclusively at detached houses! 
Amantes... I asked my friend (who has a 3-year-old) what she does when he won't settle at night. Apparently 'quiet play' involves cuddles, massage, soothing music, finger-painting, story-tapes, quiet games and toys, warm baths, walking round the garden and basically anything that calms him and does not get him excited or over-stimulated. I guess all these things take a lot more effort from the parent than letting your child run around screaming and banging on the walls!