That's awful. In any field, a writeup of a discovery should include enough information for a peer of the author to reproduce the results. Ideally, it would include enough detail for an enthusiastic amateur to reproduce the results.
This is how we write pen testing reports at work. A pen testing report written that way ~20 years ago is one of the things that got me interested in pen testing. But I apply it to all of my technical writing.
If lack of reproducibility in science is as big a problem as it seems to be, maybe journals should impose a randomized "buddy system" where getting a paper published is conditional on agreeing to repeat at least 2-3 other experiments performed by peers. Have 3 peer researchers/labs repeat the work. If at least 2/3 are successful, publish the paper. If not, the original researchers can revise their instructions once or twice to account for things the peers did differently because the original instructions didn't discuss them.
Hopefully needing to depend on the other organizations for future peer review would be sufficient to keel everyone honest, but maybe throw in a secret "we know this is reproducible" and a secret "we know this is not reproducible" set of instructions every once in awhile and ban organizations from the journal if they fail more than a few of those.
For corner cases that require something truly impractical for even a peer to reproduce independently ("our equipment included the Large Hadron Collider and a neutral particle beam cannon in geosynchronous orbit"), the researchers that want to publish can supervise the peers as the peers reproduce the work using the original equipment.
This would obviously be costly up front, but I think it would be less costly in the big picture than thousands of scientists basing decades of research on a single inaccurate paper.
I also think that forcing different teams to work together might help build a collaborative culture instead of the hostile one that's described elsewhere in this discussion, but maybe I'm overly optimistic.