From my chat with Samsung:
Stewart: Hi, thank you for contacting Samsung Technical Support. How may I help you today?
Christopher: Hello, I have a Note 3, and I am having issues where the screen becomes unresponsive to FINGER touch.
Christopher: But if I pull out the stylus, it responds to that just fine. It seems to get into this state in a variety of apps & games, as well as on my home launcher screen. Only thing that resolves it is turning the screen off and on again.
Stewart: I understand that your device screen is not responding to your finger touch. Is that correct?
Christopher: That is correct. It happens several times a day
Stewart: Thank you. I will be glad to assist you.
Stewart: Is there any screen protector on the screen?
Stewart: Thank you.
Stewart: Let us try to troubleshoot the issue by performing a soft reset in the device.
Stewart: Please follow the steps mentioned below to perform a soft reset on your Phone.
1. Turn off the handset.
2. Remove the battery and wait for 30 seconds.
3. Reinsert the battery and turn ON the device.
Christopher: okay, doing that now
Stewart: Please go ahead.
Christopher: Device is starting now
Stewart: Please check whether the issue persists after the device turned ON.
Christopher: I am checking
Christopher: The issue happens randomly
Christopher: So it may not repro right away
Stewart: If the issue persists further , you can try contacting the place of purcjase and get the device replaced under 15 days replacement warranty.
Christopher: What other reasons could cause it?
Christopher: If it happens again, is replacement the only choice?
Stewart: We do not have such reported issues at our end.
Christopher: Yesterday, it was also randomly doing the haptic-vibrate even though I wasn't doing anything
Stewart: There might be some issue with the device.
Christopher: How do I replace it? Do I take it to any AT&T store?
Stewart: Yes, please.
Surprisingly, since I did that, the issue went away. Now it's only been since yesterday afternoon that I did that, so hopefully I haven't jinx'd myself.......