In my opinion, the APA Manual is contradictory (certainly not specific enough) on this topic. My answer to your question would be footnotes (and in instances tables and graphs because it may not make sense to double space and may be confusing). A direct quote from the related link (which is quoted from the APA Manual) is: "Double-spacing is required throughout most of the manuscript. When single-spacing would improve readability, however, it is usually encouraged. Single-spacing can be used for table titles and headings, figure captions, references (but double-spacing is required between references), footnotes, and long quotations [this is sometimes referred to as block spacing]" (APA, 2001, p. 326).
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This is a difficult question to answer; but if I were to make a guess, it would be footnotes (see related link Manuscript form). Also, if you look at the Quicknotes related link, 5th bullet point down, it states where the paper may be single spaced (which is nearly verbatim from the APA manual, 5th ed. page 326 "spacing". Most institutions will require double spacing throughout.
In APA style, double spacing is used throughout the entire manuscript, including the title page, abstract, main text, references, footnotes, and figure captions. Double spacing helps improve readability and allows space for reviewers or readers to insert comments or notes.
When you quote from a source. If it is a long quote you drop down within the context of the page, center it, and single space the quote.