When pasting Set Local Variable nodes, and using right click + create variable on them, they need to be deleted and dropped in again or else there is a compile error.
It would also be really nice if pasted local variable nodes did not all have to be replaced one by one after you create them from the pasted variables name - if all greyed out variables with a certain name became valid once a variable with that name is created.
Does this occur in a clean, blank project with no additional content or is it limited to one project in particular? Was the local variable within a function of a blueprint? What type of blueprint if so? Was it in a function library? How many were you attempting to copy/paste at the same time?
I was able to reproduce this on my end and have entered a bug report, UE-21628, to be assessed by the development staff. As a workaround, create the local variable of the same name in the second blueprint before copying/pasting, instead of promoting the set node input pin to a local variable.