This if for anyone coming here as a result of their search results, regardless of which device they have. It's possible the Note® 3's stylus had a tighter fit in its slot than other Note® models, but people with other stylus-bearing models that experience this problem do pop up here and there, especially when their device is brand new. I saw it on a Note® II I had bought for someone else, and that I set up for them ( although I had owned a Note® II myself a few years ago, and it definitely did
not have that issue). What I did for the too-tight stylus was spray
just a little bit of WD-40 on a Kleenex (not directly on the stylus), then
lightly rub the stylus over the Kleenex. It immediately took care of about 50% of the problem, and I decided
not to do it again to try taking care of the other 50%, choosing instead to be content with the 50% improvement and letting the repeated pulling in/pushing out of the stylus over time take care of the balance of the problem.
There were no issues caused by the WD-40 afterward, but the key words are the ones in bold up there : "just a little bit" and "lightly", especially that second one. This is the kind of thing that, if done carelessly, will definitely wind up fcuking up something or other in the device, so if you want to try it be
very conservative with how you go about it. If you grab that can, stick the nozzle in the tube where the stylus goes :-[, and start spraying the siht out of the inside of your phone
, you absolutely deserve everything that happens after that. :'(