Psychology of disrespect and being proud of law breaking. How does it work and how to combat it? I'm gonna talk about Russia. :) I'm not interested in foreign policy, relations, for this question... maybe just a tiny bit. 

A little preamble. 
After the collapse of the Soviet Union (hereinafter S.U.), the people got lost, they didn't know who they were, what they wanted to do and who was going to tell them what to do. S.U. did a really good cleansing (of people's minds)... they were destroying all the traditions and knowledge that people lived by before S.U.: how to organize themselves, how to protect your property and even how to manage your household (if you're living in your own house). Private property, businesses, gold and anything valuable were seized. From the Party's point of view it was better if you live in an apartment rather than your own house. So, after the collapse, it was, loosely translated in English, the wild and evil ’90s. Basically the time of socio-political chaos. All the bad in people surfaced and no one to stop them because bribery was a second nature and it got instilled in the culture and the government.

Now to the point of the question. 
Nowadays, when people break laws, even those that just a manifestations of common sense and you point that out, they tend to just show "muscles" and try to scare you away. Examples: driving in places when it's prohibited, littering, bribing the law enforcement, causing disturbances (e.g. playing loud music). Driving dangerously is a particularly big problem. 

The reasoning often goes something like this: that's ok, no one's there, and it's really stupid not to take the "opportunity" (for saving little time, money, effort), I will do no harm... And even if you don't take this "opportunity", in some circles there can be social pressure to act like this. Romanticizing and glorifying a criminal life-style is somewhat prevalent... unfortunately teens often don't grow out of it. The civil court is a huge hassle (unless you're some sort of a government worker), police officers often ignore "small" violations and you left with the aggressor alone, imagine a big guy with no morals or a sociopath. 

Why people don't see that they live such an a-typical, perhaps anti-social or criminal, life? And is there a way to go about to make those people aware of how they behave?

Any terms in psychology that describe this, any books to read or forums to visit... I'll appreciate any advice.
This question can be unswered from the field of sociology.


  Sociology is the study of social behaviour or society, including its
  origins, development, organisation, networks, and institutions. It is
  a social science that uses various methods of empirical investigation
  and critical analysis to develop a body of knowledge about social
  order, disorder, and change.


Specifically what you describe here are the social norms formed by society.


  From a sociological perspective, social norms are informal
  understandings that govern the behavior of members of a society.
  Social psychology recognizes smaller group units, such as a team or an
  office, may also endorse norms separately or in addition to cultural
  or societal expectations. In other words, norms are regarded as
  collective representations of acceptable group conduct as well as
  individual perceptions of particular group conduct. They can be viewed
  as cultural products (including values, customs, and traditions) which
  represent individuals' basic knowledge of what others do and think
  that they should do.


The values and expectations that you experience are formed in the socio-economical environment of the specific nation througout many years of interactions among members of that society.

EDIT:
It is very very difficult to change deep rooted cultural habits and norms, and usually will take many years to do so. But I will give some practical advices that may help :


Lead by example. If a higly regarded individual of the society, consistently demonstrates a different behavior, this may have a long lasting effect on other members of the society and may gradually change their behavior.
Don’t push information, engage in active dialogue to change their goals and beliefs.
Changing the environment. The environment have subtle ways in which they reinforce our habits.
Create activities (like social gatherings, competitions etc) that indirectly falsify the bad sticky idea.


References of the EDIT:

Made to Stick

Smart Change

Switch