If you read scientific papers (at least in astronomy, as far as I am concerned), you will always read of a section which is called Observations and data, or similar.
There you (as author) have to explain which kind of data you used and the detailed method for data reduction.
Most of the time, this section goes along with a table in which all used data are described in detail: the observation log. The guide principle in this section is that, any reader can reproduce your results.
In the same section, information about instrument calibration is also reported in detail. Also, error sources and error determinations. Basically, everything that is included in your published data.
Of course, mistakes can happen, and sometimes we do not consider variables which are important. I do not know the details of the two examples that you mention, but they are not the first and will not be the last.
Paradoxically, what you report is exactly the reason for disproving those experiments. Both major and minor results are always tested twice or thrice or more, by different groups, different facilities/observatories, different software versions. There is no way you can guarantee for a breakgrounding result without being "differently" tested.
In the end, the method works well in this way! If I can't reproduce your results by following your description, either you are a bad writer, or your experiment is going to be confuted.
All the rest is explained well in the answer from OP @moonboy13, with the only exception that, for my experience, when data are private, they are released after 1 year.
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