I always tell my students that Revit was created for people with control issues. YOU tell the program what to do. Revit is not a one-click-wonder that reads your mind. Whatever happens, good or bad, is directly related to user input: Whether from yourself, your colleagues, or others working or collaborating with your project.
This Revit Recess post will explain the why of tag leaders "freaking out".
The image below if of an OOTB (Out Of The Box) Pipe Tag family. The red coss indicates the original position of the family reference planes. Remember that the point where the reference planes intersects, determines the base point of the family relative to your mouse curser. In other words, the family's origin point. The blue cross indicates a "finger fault", where the reference planes were unpinned and moved to this new location.
The result of the above is that the tag will be justified to the center of the label. (Note that there is quite a large space between the leader and the label. This is due to the fact that the leader end will be constrained by the blue cross)
Let's try and recreate a tag where the leader freaks out. I have unpinned and moved both the Reference Planes as well as the label I have added previously, quite a distance from the red origin point of the tag family.
The end result?
Should one of your tag family templates have been saved after the reference planes were moved (Whether by mistake or on purpose), a reinstall of the Revit content (Cringe...) should work. Alternatively, try and source an unmodified version of the specific family template from a colleague, the internet, or your friendly reseller.