Good opening, but never use Wraiths unless you are planning to use Wraiths and cloak. One wraith might be acceptable for hunting down Overlords if the opponent does not open Mutalisk. Your goal is to produce Science Vessels as fast as possible, or, in this case, to consider Valkeries which might be better for supporting your Goliaths. Do not use Goliaths to support missile turrets, even if you have the blue missile upgrade. You will keep your Goliaths in a group. You cannot split your Goliaths to support missile turrets.
The major mistake, from my perspective, is you forgot blue missiles on your Goliaths. When you are fighting Guardians, you will have the same range as the Guardian unit when you use blue missiles. Blue missiles can be upgraded after the armory is constructed if you have an add-on for the Factory.
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