How to stop a researcher cutting corners in research? Some avenues of research require time-intensive research and experimentation (e.g.m sciences). For example, in my case, each experiment took 3-12 hours and I had to perform over 30 of them.

Often, this type of research is performed as part of a group, where group cohesion and harmony are an important factor.  If you caught a member taking "short cuts" in their research: for example, doing one trial of an experiment instead of several or, as an extreme case, slightly altering the results to better fit their model. 

It is always good to speak to the person in question discreetly, but what if the behavior continues? Also speaking to them can cause disunity. 

How would this behavior be remedied, while maintaining group harmony?

(Please note, I am not after opinions, but practical solutions, particularly if people have confronted this issue before, and I have heard of this happening before, but was not privy to the details.)
I find this question very interesting but difficult to tackle. It will be difficult to provide specific answers to a general hypothetical situation since one is left with too many unknowns. First, one could wonder what the policies at the university are like? Do they have a panel for scientific fraud, misconduct etc.? Are there guidelines in place?  Then, we deal with persons and each situation is unique. People cheat for a variety of reasons from fear and feelings of inferiority and inadequacy, through stress and peer pressure to the narcissistic or psychopathic. Thirdly, the severeity of the problem is on a continuous scale and the response depends where you are on that scale. This also holds for the reverse problem, what works in one place may not work in another for these reasons.

In your question you state you wish to keep harmony but in essence the fact that "you" are uneasy with someones less than adequate research methods is already disharmony. So regardless if you do or do not do anything, there will be disharmony, either you will feel bad or someone else will. So there is no painless way out.

As for the case. I can see that you describe a sliding scale for what I would call poor science (overinterpreting results) to actual falsification of results. In the latter case, it is clear, one "must" pursue the problem. How this is done will vary but I am sure there are guidelines in place either at the university level or at a national level (on my home turf the national science foundation provides such services). 

In the case of someone producing poor science by either, for example, being too lazy to do the work or by jumping to conclusions, there can be only one way forward: to try to confront the person and have open discussions around the science (or lack thereof) to bring out the problem in the open. It may be possible to start a discussion group where you read and discuss each others manuscripts. Such discussions are useful under any circumstances to help improve the manuscript and spot problems before submitting to a journal. Under such circumstances the problems can be discussed (if they become solved is a different matter). My sense is that a person who is aware of their shortcomings is not generally fond of talking about them so you may end up having these discussions with everyone but the one you want to target.