What I know as of now:
As of now, I'm aware that you can enable access to the ServiceMode on a rooted VZW Note 3 by editing the /efs/carrier/HiddenMenu file and changing it from OFF to ON (uppercase is required).
For unrooted Note 3's, some have said there are some apps on the play store that will access the ServiceMode, but I have not been able to confirm these work.
Once ServiceMode access is enabled:
*#27663368378# takes you to the main menu where you can change various settings...most of which I don't know what they're for.
---Tips...the 'back button did not work for me and simply closed out of ServiceMode. Use the left 'Menu' key to bring up options, including 'Back'. Also, you can create a contact with the *#27663368378 number (minus the last #) and use that contact to 'copy to dialer' and save yourself from typing that number repeatedly.
To turn off Wifi Power Saving Mode:
Use either code above and at the ServiceMode screen, press the hard menu button, then select Wifi, then press the button under WIFI POWER SAVE MODE to turn it off.
To enable the new AWS band:
*#27663368378# to Main Menu, select UE SETTINGS & INFO, then SETTING, then select SYSTEM, then select NEXT PAGE and then select VZW LTEB4 ON/OFF and finally select B4 ENABLE ()...It should change to B4 ENABLE (*) with an asterisk to show it is the selected option.
-- More information specific to the AWS settings can be found here. Thanks to @milan03
What I'm not sure about:
There is a setting under the RELEASE VERSION CONTROL menu for LTE 3GPP REL 9 and LTE 3GPP REL 10. Mine was set to REL 9, but I changed it to 10 and am going to see what happens. I google LTE 3GPP REL 10 and found some documentation. Not sure why I'd want to use an previous release of anything rather than the latest release. If anyone know what this is, please enlighten me.
I'm also not sure about most of the other settings and options. Are there any that we should change to get the best performance and connectivity from our Note 3's?
There are a lot of menus and a lot of settings. My hope is that this forum can become a one-stop-shop for what they all mean and what they should be set at for optimal performance. So, please....post away!
Waiting for confirmation:
CA setting stands for Carrier Aggregation and MAY increase data speeds. See the great post from @nutpn here!
DRX CONTROL appears to be a protocol to reduce network utilization and reduce device power consumption. The question is whether or not turning this protocol off will help network connectivity and/or speed AND what effect it has on battery performance. I will turn mine off and see if I notice anything on either front. However, I live and work in an area with very good coverage, so I'm not sure that I'd be a good test case for the network speed/connectivity portion. I will definitely monitor battery consumption. This setting can be found under UE SETTTINGS & INFO, SETTING, PROTOCOL, AS, DRX CONTROL.