How to indicate when quotation marks are not used to quote someone in APA? I am careful about placing attribution to quotes in assignments. Occasionally, in assignments, I must use quote marks for purposes other than quoting, but my instructor misinterprets this as a "quote missing a citation".

In the Wikipedia article on Quotation Marks, one can find a list of examples of other uses of quotation marks. Suppose I need to use quotation marks to "signal unusual usage" ("Quotation Marks", 2014) or show some "distinction" in "usage" ("Quotation Marks", 2014) or even scare quotes. Is there any way in which I can indicate this, in APA style?
APA does not provide a distinction. It is assumed that all thinks enclosed in quotation makes are either quotes, and therefore attributed, or something "special". The hope is that your text clarifies the reason for the quotation mark. In most well written papers, the reason for the quotation marks is pretty obvious. Therefore APA style does not mandate a difference in usage.

As to why your instructor is flagging them up, it is possible your instructor is using some sort of automated system to find the missing citations or that your usage of quotation marks is excessive or improper. It is probably best to talk to the instructor to figure out what is going on.