Ultimately the problem boils down to, what gets rewarded gets done. I've previously written about peer review here
Note that my own experience with same is in areas where there is much less inherent temptation and politicization. But there are NEVER just two roaches in a kitchen.
Probably the only reasonable way to clean things up would be to have a 'loyal opposition', which made it its work to attempt reproduction and verification on large numbers of papers that are published. That loyal opposition would have to be incentivized through equivalent publication credits and availability of funding, or it'll never happen (this is why it will never happen). They'd have to be given significant funding and prestige for taking scientific scalps. At the front end, journals would have to approve experimental designs in advance and commit to accept the paper REGARDLESS of what the results were assuming the experiment described was carried out faithfully. Presently the bias introduced based on what the journals want to hear is pretty massive, especially in areas like health and medicine.