It's not usually terribly obvious that an improper merge is the cause of the problems, but that's always the first thing I look for when I see these kinds of things. Fortunately you can undo the mess and take some steps to try to prevent it occurring again.
Start on the person page for someone whose record is looking really wrong.
On the right side of the page, find the box with the title LATEST CHANGES. Click Show all to see all changes made to the record.
As you scroll through the list, you are looking for a Merge.They are easy to spot as they have a prominent green border.
Some have a blue Restore button you can click to restore the two records as they were before the merge. But many (as in the illustration above) do not.
If you do not see a Restore button, click the name of the Deleted Person.
It looks a little hopeless, doesn't it? The box says the person is deleted and so it doesn't look as if there were anything to be done. But, do not despair! Click the name in that box. The person page for the deleted person comes up. Carefully review the information on that page and decide if the merge makes sense or not. If you decide the merge was incorrect, click Restore Person in the lower right of the Person Deleted box.
Enter a Reason to Restore This Person and click Restore. That reason statement can make all the difference. If you give really good evidence that the people are not the same, you significantly decrease the chances that someone else will merge them again.
After you un-do a merge, it is also a good idea to click the Possible Duplicates link on one of the newly separated records and click Not a Match. This removes these as possible duplicates.
(Incidentally, the record I used as an illustration is not in fact a bad merge. I just needed a merged record to use for screenshots.)