Last month I completed a full implementation of Windows 2012 R2 DHCP High Availability at an enterprise organization.  
12 sites with DHCP High Availability Clustering was very straight forward to setup and document.

The following errors are specific to configuring DHCP and DHCP High Availability

Problem: Configure failover Failed. Error: 20010. The specified option does not exist.

Resolution: A pre-defined scope option needs to be setup on the new DHCP server prior to setting up DHCP HA.
Check your existing configuration in DHCP server's configuration and mirror any pre-defined scope options.


Problem: Configure failover Failed. Error: 20044. The specified DHCP class name is unknown or invalid.

Resolution: A vendor class is missing and needs to be setup on the new DHCP server prior to setting up DHCP HA.
Check your existing configuration in DHCP server's configuration and mirror any vendor class options. (this caught me due to an access point we had at a location that needed DHCP from the DHCP server.

Problem: Configure failover Failed. Error: 200103. Conflict in types for the same option on host and added DHCP servers.

Resolution: Validate there are pre-defined scope options that are conflicting. Check specifically for things like checkbox for array is checked or not checked, any vendors and/or value types are mirrored.

I hope this helps anyone who runs into these common problems setting up DHCP HA in Windows 2012 R2

Supporting Links:
DHCP Failover Settings
DHCP Server Management API Error Codes - Error codes for DHCP
Step-by-Step: DHCP High Availability with Windows 2012 R2 -easy DHCP HA walkthrough
Ensuring High Availability of DHCP using Windows 2012 R2 DHCP Failover