I've been using Carlson for over 10 years, and this thing with the points happens to me every so often. I am not changing my settings - well not doing it intentionally, that is, if that's the problem.
In some of my drawings the point block parts become separated. So, if I try to move a point to a new location, I click on the point number or the description, but the symbol doesn't move. If I then update points, it moves the coordinate to where I moved the point block, but now there's no symbol. And the symbol is still where it used to be.
If this is a setting, great. But as I said, I didn't change it, and somehow it changed itself.
I believe Carlson creates separate entities bound in a group. If your groups are off it would exhibit this behavior. On some versions Ctrl+Shift+A is the toggle, otherwise look for it in the options dialog.
Yes it's in grouping. I found the grouping terrible and turned it off in 2015. It was off in all of the other versions.
I just tried that - didn't work.
If you are running an AutoCAD engine (including the OEM) it can be found in the OPTIONS dialog, Selection Tab, left side. Or you can use the PICKSTYLE system variable, it should be set to 1 (or higher).