I was not concluding it was defective but that's certainly a definite possibilty.
So no magnetic case.
Turn on the on screen pointer and try hovering all areas.
You can try a new nib with the supplied tool. I had to when the pointer was off to the right, and it improved. (you can squeeze, pull and push them in and out ss hard ss you like!)
Try clearing the cache of each app you use for that in the App Info. Sketchbook/S-Notesm/Action Memo etc. Then clear the app data also.
General - Applications Manager - scroll right to All.
Wipe the Cache Partition in Recovery mode.
http://forums.androidcentral.com/showthread.php?t=298808
It's hard to define how fast you mean. Does it write normally at writing speed.
If you get no further input here, and (AT&T) * sorry T-Mobile like Verizon lock you out of settings, I would seek a check up from a service rep or call them.
I am not a site ambassador so I am just relaying my related experiences and what I have read of S-Pen issues in threads over 8 months. It is possible I have missed something.
In fact those that know me would say that is usually a given!