Is there a term for unconsciously using a wrong word when speaking because you were otherwise looking at, listening to, or thinking about that word?

This would most generally be called a slip of the tongue. These are sometimes called Freudian slips, but that really describes a specific circumstance in which the words you say belie some unconscious thought or desire. You'll often hear the term used without its proper psychoanalytical context to describe any slip of the tongue, though.

I'm still doing a bit of research, but here's what I've come up with for now -

Echolalia

Echolalia is the unsolicited repetition of vocalizations made by another person (when repeated by the same person, it is called palilalia). In its profound form it is automatic and effortless. It is one of the echophenomena, closely related to echopraxia, the automatic repetition of movements made by another person; both are "subsets of imitative behavior" whereby sounds or actions are imitated "without explicit awareness". Echolalia may be an immediate reaction to a stimulus or may be delayed.

Source - Wikipedia

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Echolalia: The involuntary parrotlike repetition (echoing) of a word or phrase just spoken by another person.

Source - medicinenet.com

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There's also mirroring -

Mirroring is the behaviour in which one person subconsciously imitates the gesture, speech pattern, or attitude of another.

However, this doesn't really suit the purpose of this question very well...

From Wikipedia -

Mirroring generally takes place unconsciously as individuals react with the situation. Mirroring is common in conversation, as the listeners will typically smile or frown along with the speaker, as well as imitate body posture or attitude about the topic. Individuals may be more willing to empathize with and accept people whom they believe hold similar interests and beliefs, and thus mirroring the person with whom one is speaking may establish connections between the individuals involved.