I have Linux Mint 17.1 KDE installed, which automatically boots to desktop. I use an external monitor and have the laptop's screen blanked.

About 1 time in 3 KDE fails to start properly. The laptop's screen is active and no external monitor, and the panel's configuration is not right. The 4 virtual desktops are on one line instead of 2.

Logging out and back in does not give a usable desktop.
A reboot is required, and almost always starts correctly.

I have /home on a separate partition.

Is there a race condition somewhere?

Is the /home partition on the same physical volume or on a separate volume?
It may be possible that the the /home partition is not mounting fast enough, especially if it's on a separate media device.

I don't use KDE but I know I had to increase start-up delays for some software on my system which also uses an external monitor with the laptop monitor blanked. This was easy for me to fix as I'm using openbox but I'm not certain how KDE handles start-up sequences.

It's on the same physical volume. I thought a slow mount might be the problem so I duplicated the configuration parts of my home directory at the mount point so it should not matter.

I will try putting a 5 second delay before startkde and see what happens.