In yet another report worth seeing both for the factual content and the entertainment value, John Oliver addresses some problems with science, including insufficient replication, doubtful forced results ("p-hacking"), and especially sloppy science reporting in the media, notably on morning news shows.
Incidentally, for more on the subject of p-hacking, see this XKCD comic and accompanying explanation.
The problems Oliver describes have lately been a major topic for discussion in the scientific community, and serious efforts are being made to address them, so it's not like they're being ignored. But it's not necessarily clear what to do, and some in some fields it's just inherently harder to get sound results. Research related to human beings, from health to sociology, is particularly difficult.
As Oliver suggests, one of the biggest problems with bad science is that besides simply being misleading, it can cause unjustified public doubts about really sound science. There's a big difference between isolated individual studies with questionable results (or with results wildly exaggerate or completely misrepresented by the news media) and immense bodies of research and evidence for things such as evolution, global warming, and quantum mechanics. But for many non-scientists the distinction isn't clear.