There are many scientific themes and ideas that are explored in this brilliant film, and I am only going to be able to indicate a few in this response. I have included a link below to an article that should hopefully give you more ideas, but my response should give you enough to get you started in responding fully to this question.
The central scientific idea that creates the basis of this film is the creation of artificial intelligence. We are presented with a dystopian world where science has become so advanced that humans are able to create replicants, robots who are so similar to humans that only a lengthy test examining the involuntary dilation of the pupil in response to a series of questions is able to determine whether somebody is human or replicant. This of course is used in the film to raise massive philosophical and ethical issues, as the central question that is debated is what makes us human and how we should treat those we consider to be "non-human."
Aside from this issue, however, there are other significant scientific issues. You might like to consider the emphasis that is placed on off-world colonies. Mankind is now colonising other planets and in a sense, leaving earth behind. Only humans who have health issues are not able to leave earth, resulting in the remaining cities becoming full of miscreants and n'er-do-wells.
In addition, the picture we are given of LA in the future is one that would terrify environmentalists. Cities are constantly surrounded by clouds of smog that shroud them in perpetual darkness. Environmentally, it is no wonder that there is such an emphasis placed on colonising other planets in space, as, it is suggested, humans have almost completely used up the earth's resources and need to move on to somewhere else.
These are just some of the scientific issues that are raised in this excellent film. I hope this helps you begin to answer this question. Good luck!