Affect vs. Effect: This is an old one, but still worth reviewing. As a noun, effect means "result": The effect of the terrorist attack was war. As a verb, it means "to accomplish" or "to cause": To effect power, we must take it with force. Effect will also be used to convey vague ideas, such as, The climactic effect, its subtle effects, or, if you really want to be annoyed: Its subtle effects affected me. But please don't write such a vague sentence.
Affect, on the other hand, means "to influence": His rhetoric deeply affected one student, who later would become president.
Allusion vs. Illusion: To allude is to make an indirect reference. An illusion is something that is falsely perceived. Steinbeck's East of Eden holds strong biblical allusions. The Fata Morgana we saw is a complex visual illusion.
That vs. Which: That is restrictive—what follows is necessary to understand what came before, while which is nonrestrictive, and should follow a comma because it introduces a parenthetical statement. The car that I bought is at home (this determines what car we bought). The car, which I bought, is at home (the car is at home, and the fact that I bought it is unnecessary in this case). You'll notice it depends on what's important in the context. As shown above, the fact that I bought it might or might not be important. It depends.