[UNDER CONSTRUCTION]
So, what is a merger?
Taking the answer from the official FAQ: "The AI that guides Eyewire is good, and constantly improving, but not perfect. Once in a while it does stick two things together that do not belong."
However there are also cubes where the images are very blurry/fuzzy and players create connect two pieces that are in fact belong to different cells.
What should I do when I spot a merger?
That depends on the size and even more on the position of the merger: Small ones in the midst of a cube are not that important - luckily, because they occur pretty often. Especially at Starburst Challenge. If you add them to your solution or leave them out is pretty much up to you. I usually decide depending on if the correct part is bigger than the wrong part or not.
Potentially harmful however are mergers somewhere in the mid of your path that extend to the cube wall. If enough players add those to their solution it will spawn a new cube on the other side of the wall. And in this case you and all the other people have no chance to see that this was in fact a merger from the neighboring cube. So never add those to your solution!
And I would say there is a third category - let's call them "the unavoidables": Mergers where neither you nor the AI got suspicious, seed pieces that already contain a merger and also "exit point" pieces that contain a merger. If you everyone would skip those, the cell can't grow any further, which is in some cases even worse than a merger... Those are the ones you can also see in the overview. They keep growing and spawning new cubes until the GrimReaper arrives. That is the reason why our dear GrimReaper put a bounty on them! The link also contains a description how to report mergers. Remember: Only mergers visible in the overview - not the boring and easily avoidable ones ;-)
Pictures of the above mentioned mergers?
In many cases the wrong part that the AI adds is really small and in the middle of the cube. For example this one spotted by @jinbean:
The yellow part is added with a single click and could mislead somebody into following the red branch as well - and will turn a harmless AI-merger into an ugly player-made. The Explore Mode can help to identify this uncommon shape (two parallel paths).
The next one is one of the mergers where a part extends to the cube wall:
That might not be a perfect picture for what I mentioned in the text above - but I think you get my drift. You should leave those pieces out - even if that means you have a small gap within your path.
A merger that was visible in the overview (Starbust Amacrine Cell) - that's one where the GrimReaper has to step in (You can enlarge those pictures when you click on them at the bottom of this post):
