Does science have limitations?
Science itself is a limitation. It is inherently limiting because it must yield observable, testable proof. This is not to say that science is useless; it has done many beneficial things for society and humanity the world over, but it is limiting.
For example, "hard" science does not acknowledge anything that cannot be directly observed. However, there are many instances in which people experience "abnormal" phenomena which is ignored, even denounced by the scientific field. Whether these things are true or not, science cannot test for these things within the limitations of its framework, so it just ignores it.
One current example of this is the study of consciousness. There are many articles (esp. Pinker's work) which seek to answer the question of "what makes reality, real?" Studies are pointing to the notion that reality is a subjective, NOT objective, phenomena. What this means is that your reality is shaped by what you believe, what you've experienced, and what you know to be true. If you believe yourself to be dumb and lazy, chances are you will create that reality in your life and manifest the circumstances which perpetuate what you believe about yourself. If you believe you are destined to live a life free of limitations and boundaries set against you, then you will see the opportunities open up to you and make that your reality. The same principle is true with science. It is a self-limiting practice to only test for what we already know to be true, because we stifle the opportunity for growth by focusing on what's already there.