What are three examples of wordplay in The Handmaid's Tale?

At one point, Offred says, "I compose myself.  My self is a thing I must now compose, as one composes a speech.  What I must present is a made thing, not something born."  Here, she plays with the word compose.  When we say that someone composes a speech, we mean that the person writes and prepares it.  When we say that someone composes herself, we mean that she collects her thoughts and feelings and presents an image that seems put together, so to speak.  Offred seems to mean that she composes herself in both senses of the word: she attempts to collect and prepare all the fragments of her person under the Gileadean regime so that she can present herself as something that seems practiced and natural and polished, not awkward and strange.

Another time, when the Commander hands her a pen during one of their clandestine meetings, Offred recalls a memory from the Red Center.  She says, "The pen between my fingers is sensuous, alive almost, I can feel its power, the power of the words it contains.  Pen Is Envy, Aunt Lydia would say, quoting another Center motto, warning us away from such objects."  Penis envy is the Freudian idea that women are naturally envious of men's penises because the penis is the source of power.  Here, Offred plays with the letters, breaking them up differently to say "Pen Is Envy" because the ability to read and write has become an incredible source of power for the Commanders of Gilead.  She envies her Commander his right to the pen, something that she lacks.

When Offred describes Moira's escape from the Red Center, she says, "Moira had power now, she'd been set loose, she'd set herself loose.  She was now a loose woman."  Loose has several potential meanings here: Moira has been released or set free, but her pieces also seem to have come loose as though she's in danger of losing some now that she's no longer confined and defined by her societal role.  Further, to be a "loose woman" is a sort of old-fashioned way to describe a sexually promiscuous woman.  Taken together, Moira is both dangerous and endangered, which is just how the leaders of Gilead would want the other handmaids-in-training to think of her.