Step 1: Understanding the Concept:
This question tests the knowledge of commonly confused words, specifically homophones or near-homophones. The choice between 'illusion' and 'allusion' depends on the intended meaning in the context of a poem.
Step 2: Detailed Explanation:
Let's define the two words:
Illusion: A false idea or belief; a deceptive appearance or impression. (e.g., an optical illusion).
Allusion: An indirect or passing reference to a person, place, event, or another literary work. (e.g., a biblical allusion).
In the context of a poem, which is a literary work, it is highly likely that the author is referring to indirect references ('allusions') rather than false perceptions ('illusions'). An 'obscure allusion' would be a reference that is difficult to understand.
Therefore, the word 'illusions' is used incorrectly. The correct word should be 'allusions'.
The corrected sentence would be: "The poem has many obscure allusions".
Step 3: Final Answer:
The word that is an error in the sentence is illusions.