Stanley's suspicion of Blanche’s past foreshadows his obsessive rooting-out of all she is hiding. When she arrives in New Orleans, he goes through her suitcase, showing jewels and furs to Stella and yelling hyperbolically:
STANLEY: I've got an acquaintance who deals in this sort of merchandise. I'll have him check on it...Here’s your plantation, or what’s left of it, here!
When Stanley declares that he's holding "what's left of" Stella's "plantation," he means that he believes the dresses and furs inside Blanche's suitcase are proof she has been cheating him and Stella out of money from selling Belle Reve. When he sees all of Stella's rich, brightly colored silks and jewels, Stanley immediately assumes that they must be worth a lot of money. As soon as he sees her furs, he's completely convinced she's stolen all the profits he believes selling Belle Reve must have made. Of course, it's impossible that a few dresses and furs would be worth as much as a house and its property, but Stanley is angry enough to exaggerate as he screams at his wife. Stanley also can't tell real jewels and silks from costume tiaras and nylon.
Despite this, his explosive anger when he sees Stella's possessions and his willingness to involve his community in exposing her foreshadow his obsessive suspicion of Blanche's motives. Even though Stanley isn't sure of the value of the clothes and jewels himself, he's willing to share his suspicions about his wife's sister with "an acquaintance" immediately. He goes from calmly questioning Stella to shouting almost immediately in this scene, which also foreshadows his explosive anger. His shouting is accompanied by throwing the contents of the suitcase all over the floor and into Stella's face. His violent, highly physical anger even extends to his interactions with clothes.
Throughout the play, Blanche does whatever she can to avoid being exposed to bright electric light. The way she shrinks away from it whenever it appears foreshadows her dread of any kind of exposure. At the beginning of the play, she tells Mitch flirtartiously that:
BLANCHE: I can't stand a naked light bulb, any more than I can a rude remark or a vulgar action.
Blanche says this to Mitch the first time they converse. She purrs this sentence coyly to him as she asks him to cover the bare lightbulb in her room with the paper shade she's bought for the purpose. In doing so, she makes him complicit in helping her avoid the bulb's strong light. She's also warning him that she has certain expectations for the behavior of the people around her, even at this very early stage.
This moment foreshadows several important events that follow it. It's the first instance where Mitch unquestioningly does as Blanche asks him to, which tends to be how he behaves later on in their relationship until it collapses. It is also a moment where Blanche draws a direct link between the presence of light and the way that she detests "vulgar actions." Blanche's delusions about herself and her world depend on a certain amount of wilful avoidance and obfuscation. By asking Mitch to help her cover up the bulb, she's inviting him to join her in her fantasy life. When Stanley squashes Mitch's illusions about her, he tellingly references the paper cover again, as if to imply he understood Blanche's intentions in this scene.