Some words are tricky. For example, students new to art history have to learn that formal analysis means an analysis of form, and has nothing to do with formal dress. But that's an easy one. Once learned, it's seldom forgotten. More troublesome are pairs that are easily confused and that frequently appear incorrectly in print or on the internet, reinforcing people's mistakes.
Tenants and Tenets: A tenant is someone living in a space, a tenet is a foundational idea.
Simple and Simplistic: Simple is... well, simple. Easy. Uncomplicated. Plain. Simplistic refers to a notion someone has simplified to the point of being rather stupid. Simplistic explanations are not good, simple ones may be.
Compliment and Complement: A compliment is when someone tells you you're smart or they like your sense of style. A complement is an addition, generally of a positive sort. For instance, your new shoes may complement (add to and go with) your wardrobe, but as they are not animate, they do not compliment it.
Phase and faze: A phase is time related; we can refer to a phase in someone's life or career. When you are fazed, you are generally disturbed by something (one more often says that a person was unfazed, meaning the disturbing event or situation didn't seem to bother the person unduly).
Affect and Effect: To affect something is to have an effect on it. (Yes, really!) Affect is also a psychological term referring to how someone presents him/herself ("depressed affect"), but this sense is unlikely to be used in art history. One can affect change (pretend change or have an effect upon it) but more often one will effect change (make it happen). The two words are devilishly similar in some of their meanings, and more troublesome in that Effect is often carelessly pronounced just like Affect (as if both were spelled Uffect). Also, the psychological term Affect stresses the first syllable, whereas otherwise the stress is generally on the second.
Handy guides include
Carnegie Mellon's Tricky Words
Alan Cooper's Homonym List
Please add more of these in the comments section!