Thank you for waiting. It's going to be impossible to give you a definite answer based only on an online description, but I'll give you some possibilities. But before I do that, despite our mutual dislike for giving up on a plant, my first recommendation to you is to return the tree.The reason for that si that you will either need to do some detective work first or experiment with treatments. In the end, you may well lose the avocado anyway.
That being said, I'll tell you some possibilities. The white splotch at the base is probably the result of a fluid the plant leaks form minor injuries. In that case, it's nothing to worry about. The other possibility is a fungus.
Now for the leaves. Phytophthora root rot, also called cinnamon root rot, is very common in California. Although the pathogen is in the roots, the leaves are often first to show the effects. They become splotchy and holes develop, then they die and fall off. There are systemic fungicides that give some control of this disease. They would be available at local nurseries and garden centers. Deficiencies of minerals can also be responsible. A fertilizer containing both macro and micro nutrients would remedy that problem.Mites can also do the same thing to the leaves. They are such a tiny species that we often can't detect them. However, they do usually make webs on the underside of the leaves.
At this point, you're probably wondering what to do. If you choose to keep the avocado, I suggest that your next step be to contact your County Extension Agent. This is a government program offered through universities, and there is no charge for their services. Just click on this link, then click on your county to get contact information:http://ucanr.edu/County_Offices/
In some areas, the agents will come to your home to examine a plant, while in others, you'll have to deliver a leaf for them to look at. They won't treat the plant for you, but they will diagnose it and recommend a treatment.
If you have more questions, let me know by clicking on REPLY. I hope the situation works out well for you no matter what you decide to do.