Science Myths: Some things can't be tested by science
While it is fair to say that some things cannot be tested by science, in reality this is rare—there are very few things which cannot be examined using the scientific method.
Firstly it is important to understand what is meant by "science". Science does not always involve experiments and lab coats, in fact most science does not. Science is simply a process of investigation that follows certain rules to make sure there are no mistakes or cheating. Some scientific investigations are very simple and may involve little more than counting numbers.
Here's an example: It is often said that psychic ability cannot be tested by science, but consider this: If a psychic claims that she has a 97% success rate, how did she arrive at this figure? Presumably by defining "success" and then counting the number of successes versus failures. Although she may not like to admit it, this is science. The process of arriving at such a percentage can only be achieved by some sort of systematic evaluation, which is exactly what science is. For a psychic to say "I have a high strike rate but you can't test it scientifically" is a self-contradicting statement.
Importantly, if the psychic in the above example has a poor definition of success, or fails to count successes and failures accurately, the results will be flawed. However it is the implementation of science that is at fault, not science itself.