I have two ATT note 3's, my own, which is on 4.3 and rooted, and my wife's is completely stock. Mine tried to do the OTA update but fails to complete, most likely because I'm rooted, I'm guessing. Her OTA went through and she was updated to 4.4.2. Since the update SMS appears to send out fine from the phone, but never actually does based on testing. The APN settings initially reverted back to AT&T, so after setting that back, mobile data worked fine again.
We both recently ported from AT&T to Striaght Talk and use an AT&T Microcell in our home. It has all been working well until the 4.4.2 update to her phone, that's all that changed.
I have tried quite a few different APN settings but have seen no change. Right now I am not sure if this is an Android issue or Straight Talk issue. I've done the very obvious things like rebooting the phone, I'm just unsure on what the next troubleshooting steps would be, other than contacting Straight Talk or googling these symptoms, but it's just a very broad problem to find a specific fix for.