Like so many things, the question of whether psychology is a science is a matter of degree. Does it seek out and discover new information by applying the scientific method? Are its findings based on empirical data that can be verified by others? Does it emphasize empirical evidence and discard those theories at odds with carefully controlled experiments? Does it emphasize parsimony and accept the burden of proof in supporting its theories? Does it support empirically validated findings even when they are unpopular or contrary to what everyone believes? Does it insist on verifying results by replication?
To the degree that psychology can answer yes to these questions, it is a science.
On the other hand, there are many areas in psychology that fail to meet these standards. In many cases these shortcomings arise from the complex nature of the subject matter rather than a lack of professional attention to detail or indifference to scientific methodology. Clinical psychology (my specific background) is one of the most problematic in this regard because it deals with content that is hard to empirically observe. It's not like you can call some colleagues over and ask them to take a look at the crazy thoughts your patient is having! Because of this, a clinical psychologist is often reduced to the unscientific practice of introspecting by analogy (“You must be thinking that. . .”). Because clinical psychology is a big part of what the public thinks psychology is, the perception of psychology as a science is diminished.
Another scientific problem for psychology is that human behavior is affected by so many unobservable and difficult-to-control variables. For example, take attitude. When you give human subjects instructions in an experiment they may outwardly appear cooperative but inwardly be thinking "Kiss my kiester!" (“Kiester” being the technical term for “buttocks.”) The kiss-my-kiester attitude will clearly affect your results but you will never know it's there. And if you do, how can you control for it? Do you order your subjects to be cooperative?
The physical sciences — chemistry and physics — never have to deal with these variables because rocks and chemicals don't have attitudes and don't get stubborn or try to fool you.
So in answer to the question of whether psychology is a science, like so many things, it's a matter of degree. It is — sort of. . . somewhat. . .kind of.