I have a Thuja plicata "Green Giant" that has a crooked trunk. Is it doomed to have issues at some point? Is there anything special I should do when I plant it?
Your Green Giant can attain a width of at least 12 feet, so you'll never notice the crooked base after a few years - assuming that the area at the base of the plant is relatively weed free so that the branches aren't shaded by competition. Even if you limb it up at some point, the crookedness will impart some architectural interest to the trunk.
I would plant it just like it is in the pot, with the crook at the base. Do not cover the trunk with mulch in an attempt to hide the "defect".
Given the size of the trunk relative to the pot, I'd get that tree in the ground ASAP, if possible. You may want to consider "bare-rooting" the tree, even though it's in a pot. This is a method pioneered by Dr. Linda Chalker-Scott - after you remove the tree from the pot, you immerse the root ball into a bucket of water and gently agitate it/use your fingers to remove all of the soil from the root ball. This will give you a mass of roots that you should be able to spread out - so, you dig a wide hole, not a deep one. This method can work well with shallow-rooted trees and shrubs like your arb (if you don't bare-root the tree, the the tree has to redirect/replace the roots buried as part of the root ball with roots that are much closer to the soil surface. This is sometimes why a transplanted tree can take 3 years to get established). If you're interested, here is much more information: 'Take It All Off!'