How is psychology as a scientific discipline similar and different to casual observations we make in everyday life?
Psychology, as the question notes, is a scientific discipline that incorporates observations, but places those observations within a specific context. A textbook definition of psychology can be "the scientific study of how people behave, think and feel." [What is Psychology?" The University of Queensland, School of Psychology, Australia]. Psychologists attempt to understand what makes individuals think and act in a certain way so that those who experience difficulties acting within the conventional parameters of society or adjusting to unfamiliar environments can be helped to better function.
Whereas the casual observer of human behavior can attain a certain level of knowledge through his or her observations, he or she usually lacks a broader intellectual framework with which to understand that behavior and devise corrective measures when warranted. The study of psychology includes not only theoretical readings that help students understand the history of the field of psychology and enables them to learn about patterns of behavior researched by others, it also requires them to conduct their own experiments on both animals and on human subjects to witness for themselves how living creatures respond to certain stimuli or act under certain controlled situations, for example, during periods of intense stress.
It is entirely possible for a "layman" to develop the skills to understand human psychology. The assessments of such an individual, however, have to be accepted for what they are. There is a reason practicing psychologists are licensed: they demonstrate that they know the field from a scientific perspective, and are met certain qualifications -- qualifications not shared by casual observers of human behavior, no matter how observant those individuals may be.