Now:
The term plugin refers to a user-agent defined set of content handlers used by the user agent that can take part in the user agent's rendering of a Document object ... .

Suggestion:
The term plugin refers to a user-agent defined set of content handlers that can be used by the user agent. The content handlers can take part in the user agent's rendering of a Document object ... . 

Comment:
Simple short sentences are nice for people with great HTML abilities but an average knowledge of english grammar.

Now it could be interpreted as:
User agent 1 (helper) defines content handlers.
User agent 1 (helper) uses content handlers.
User agent 2 (mother, browser) gets help by user agent (helper).

If you refer with 'that' in the above sentence to user agent, the closest choice instead of content handlers (which is far away) the meaning of the sentence is different.

If you read these sentences as a non native speaker or even as a translator, the minimum damage is that it costs extra time to understand it, the worst is that it is understood wrong.

Many times I cut a sentence which runs across a paragraph into two to six sentences to make the translation simple to understand. - Cite: to draw attention to the specification and to promote its widespread deployment. There is a catch in that sentence.