I'll edit this and add new fixes as I see new errors appear.
1) Crashing to Desktop / "Unable to load surface prop file 'scripts/surfaceproperties_ep2.text' (referenced by manifest file 'scripts/surfaceproperties_manifest.text')"
The mod requires the content from Half Life 2: Episode 2 to be installed. If you still get this error, try running Episode 2 (just the main menu, you can quit when that pops up), then running the mod again.
2) An error referring to the "Library Client" or "Engine Mount". Happens before the mod launches.
Sometimes when the Source engine is updated, the mods don't update with them; the games need to actually update their files. To fix this, simply run Half Life 2: Deathmatch (just getting to the main menu is fine, no need to create or join a server). Then try running Zombie Colony again.
3) The mod refuses to start, yet you have both games installed
It may have not downloaded the 2007 branch of the source engine automatically. To get this, simply select "All Games" and change it to "tools", then scroll down and install "Source SDK Base 2007".