It's not an answer to your specific intermittent failure, but I do have a workaround that several clients have used.
I make them another account that isn't file vault protected and rather than logging out and leaving the mac at the welcome screen, enter the empty user and walk away. (or kick off a backup and then walk away)
In practice I get better backups when a user is logged in.
If this needs to work for you, do file a bug with apple since it should work each time and every time without a workaround. When it fails, there should be detailed enough logging to fix issues if they arise even if normal logs are suppressed as a compromise to added security with FileVault enabled.
Also BackupLoupe is great for poking at backups to see what is actually changing after the fact rather than guessing from logs and byte counts stored in logs.
I have had other people reconsider file vault and just use encrypted disk images for data that needs to be secured which minimizes many of the drawbacks of having the entire user folder inside file vault. I've done this myself since soon after file vault came out and I much prefer it compared to living with FileVault.
The whole "root" directory you picture, and finder shows actually does not exist at all. It's kind of a "meta" directory. The unix root directory (e.g. /) points to the folder OS X calls "Macintosh HD". Everything is a sub-directory of that, even other drives.
Basically, when you connect a external drive, insert a CD, mount a DMG, or map a network drive, the resources contained within the new drive are actually made available (called "mounting") as a subdirectory of /Volumes/[Drive name here].
Finder (and finder only) has a facility that shows a fake-directory that contains all the mounted drives.
In other words, the reason you can have two home directories is because they're not actually in the same folder. One is actually located at /Volumes/home and the other is /home.
Anyways...
The home and net directories actually exist as folders on your main drive. If you open the root directory of your drive (IN your picture, its labeled "Macintosh HD"), you'll see where they are actually located.
The home directory seems to be related to enterprise environments, where various network drives can be defined using a directory service. I believe that, in such a situation, the automounted drives appear in /home/[Network drive name], rather then the OS X traditional /Volumes/[Drive name]. In any event, it's part of the autofs underpinnings of OS X. More here.
The /net directory also seems to be related to the automounter. There is a thread about it on the apple support forums here.
/net is built into the automounter in OS X and uses the special map
-hosts. This built in map will consist of the exports from the named server, when that server is accessed via the /net path. For example,
if I have an NFS server at the IP address 192.168.1.10 and it exports
a directory /exports, then if I do this from my Mac:
prompt$ cd /net/192.168.1.10/exports
the Mac automounter will contact the server, mount the export, and put
me in that directory. All without me having to issue any "mount"
command.
As such, it may be possible to use the /net directory as a shortcut to access network drives, assuming you're working from the command line. It doesn't seem to work for SMB (i.e. windows) shares (at least for me), though.
Incidentally, if you want to look at what's mounted where, all you have to do is open a command-prompt, and type mount. It will return a list of all the drives your computer has, and where they are mounted.
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