What is the phenomenological critique of science?
Phenomenlogy is a philosophy that strives to have a more objective understanding of the world by acknowledging the subjective nature of experience. Therefore, much reflection is required by the scientist on his/her individual conscious apprehensions of the world. The roots of this philosophy are found in Kant who described things as they appear (phenomena) and things in themselves (noumena) or things as they actually are.
What phenomenolgists try to do is understand the ways we consciously observe the world and how our mental acts have intentionality. This means that a mental act has an "aboutness" which is to say that a thought can be about an iceberg but a physical object like an iceberg is not "about" something. This separates physical objects and mental acts, something the phenomenologist would insist that scientists be aware of.
Even if we discuss objects in terms of objective theories, based on physics and math, our discussion is a mental activity. The phenomenologist would criticize the scientist who only considers the objects he is studying. The phenomenologist would implore that scientist to consider how his individual (first-person) conscious experience plays a role in apprehending knowledge about that object. For example, if I see a yellow tennis ball, half of which is in shade, it appears not to be uniformly yellow. But the thing in itself (outside the shade) is a uniform yellow. Here is an example where individual conscious experience is a limit to gathering knowledge.