[Verizon Galaxy Note 4 Q&A, Help & Troubleshooting] azumandias:
Hello, I am posting this as a potential service to other flash happy DE owners. It may be obvious to some but I had to compile a number of semi-related Google searches to come by a solution for my issue.

I have been happily playing with my new DE and flashing our one ROM along with Xposed and a few modules. Everything was going just fine until I started having the phone reboot after a minute or so of starting up. I found that if I had Airplane Mode enabled it would boot just fine. Long story short, my phone would reboot every time AdFree tried to update the hosts file (evidently within a minute of the phone starting up if there was any sort of internet connection).

While trying to debug this I disabled Xposed and its modules as they can cause all kinds of problems - to no avail. I also tried re-flashing the ROM in TWRP and TWRP crashed and rebooted just as AdFree was doing. I then re-downloaded the ROM and rechecked its MD5 signature. Once I knew I had a good download, I again tried to flash it in TWRP and again my phone rebooted.

Again, long story short (too late!), I finally realized that my phone was rebooting anytime something tried to alter the /system partition. Some more Googling led me to a suggestion to check that partition for errors. To do this you must first boot into TWRP. Then connect your phone to your computer. If the phone doesn't install properly, go to Device Manager, you'll see under "other devices" an Android ADB with the yellow exclamation mark next to it. You "update drivers" and choose the drivers to install - choose Samsung ADB or Samsung ADB Interface. Now the device is recognized from TWRP (thanks unkellsam for outlining this). Our /system partition is /dev/block/mmcblk0p24 but owners of other devices can run the following commands to discover their /system partition (thanks android927 for outlining this):

adb shell
ls -al /dev/block/platform/*/by-name

Once you know your system partition, run the following code (leave out the "adb shell" if you have already run it and replace "mmcblk0p24" with your own device's /system partition if you don't have a Note 4 DE):

adb shell
e2fsck -fv /dev/block/mmcblk0p24

For me this produced the following results:

Pass 1: Checking inodes, blocks, and sizes

Pass 2: Checking directory structure

Entry 'feature.xml.bak' in /csc (8021) has deleted/unused inode 2671. Clear<y>?

Entry 'PowerOn.ogg.bak' in /media/audio/ui (2449) has deleted/unused inode 2672. Clear<y>?

Pass 3: Checking directory connectivity

/lost+found not found. Create<y>?

Pass 4: Checking reference counts

Pass 5: Checking group summary information

Free blocks count wrong for group #2 (1613, counted=1618).

Fix<y>?

Free blocks count wrong for group #5 (325, counted=337).

Fix<y>?

Free blocks count wrong for group #8 (1382, counted=1377).

Fix<y>?

Free blocks count wrong for group #20 (895, counted=913).

Fix<y>?

Free blocks count wrong (395151, counted=395181).

Fix<y>?

Free inodes count wrong for group #0 (5345, counted=5346).

Fix<y>?

Free inodes count wrong for group #16 (6741, counted=6742).

Fix<y>?

Free inodes count wrong (252552, counted=252554).

Fix<y>?

/dev/block/mmcblk0p24: ***** FILE SYSTEM WAS MODIFIED *****

3958 inodes used (1.54%)

48 non-contiguous files (1.2%)

4 non-contiguous directories (0.1%)

# of inodes with ind/dind/tind blocks: 0/0/0

Extent depth histogram: 3869

653395 blocks used (62.31%)

0 bad blocks

0 large files

3692 regular files

176 directories

0 character device files

0 block device files

0 fifos

0 links

80 symbolic links (80 fast symbolic links)

0 sockets

--------

3948 files

I said yes to each of the repair questions then ran the file scan again confirming no further errors. Booted back up and AdFree wrote the hosts file just fine.

I hope no one else runs into this kind of error but I hope this is helpful if someone else has similar issues.

I am a little concerned about the potential for a bad batch of memory in my phone but the scan did say no bad blocks so I am hoping it was just a bit of file corruption from my flash-happy weekend. Anyone else want to chime in on whether I should be worried about actual hardware failure?

Thanks