New Improved Merge Experience (courtesy of RootsTech)

I have done a lot of merging. It is often needed, but I appreciate the need for caution. A bad merge can make a big mess. Sometimes the very best answer is "Not a match." But not always. 

Deciding When to Merge
To what extent do the following things match?
Names, places (are they less than 10 miles apart?), dates, relationships (do they have the same children?)
Note that information on the children is normally more detailed than information on the parents. Are the children of the possible duplicates born in the same place in the same time period?

If they fail these tests, I would mark them as "not a match". If they pass these tests I would merge them.
If it is unclear, I would seek guidance through prayer, which tends to result in "not a match".

A BIG UPDATE:
I tried out the new Improved Merge Experience, announced in RootsTech.
See the explanation and the buttons at www.familysearch.org/labs
And take a look at this 10-minute video of me learning to use the new process.
Maybe try it with some of your "possible duplicates".
https://youtu.be/F9tRBHqbfiY

Correcting a Bad Merge
Recently I discovered that my 2xGGPs were incorrectly merged with a different couple with the same names living 30 miles away, in the next county. As I studied the Sources and the Changes log, I could see what had happened, and how I could separate the records of the two families. The Undo Merge option was unavailable, but I could RESTORE the people deleted by the merge, and then move children to the correct parents, and detach sources that referred to the wrong people. 
I made a 26-minute video demonstrating the main parts of the process. If you suspect relationship errors in your part of the family tree, start with an analysis of the Sources and Changes. Include prayer in your decision. More research may be needed. If you decide to proceed, this video may help. https://youtu.be/kWB6aAbBZbw

Correcting Data Errors in Family Tree
Correcting factual errors is usually super easy. (Click the pencil icon, replace the incorrect data, and Save.)
Correcting relationship errors is more complex but this video may help.

This video by Aimee Cross may also be helpful. To Merge or UnMerge, that is the question (FamilySearch Tutorial)
https://www.youtube.com/watch?v=6V99HfzeBts