Amphiboly

Amphiboly (Web) is creating an ambiguous premise with poor or misleading grammatical construction.

Philosophy Pages has a great example.

Bruce Thompson:

The argument depends upon an ambiguity in grammar. One meaning makes one of the premisses true, but it makes another of the premisses false. The alternative meaning makes the second premiss true, but makes the first premiss false.

Fallacy Files suggests that typically the ambiguity is in abuse of pronouns or descriptors that could apply to either the subject or the object in a sentence.