This is a very interesting question. To understand the symbolic significance of Mrs. Hutchinson's apron, let's first review the symbolic import of the faded dresses and sweaters ("wearing faded house dresses and sweaters"). Throughout, the lottery is symbolically identified as a faded and worn out ritual. Steve Adams even explains that in some places, the lottery was being abandoned altogether (though this enlightening information ironically doesn't stop him from being in the fore-guard during the attack of the resolution). The box is described as being in a worn out condition without benefit of repair or paint. It has no permanent storage location between annual usage; it is even underfoot: "another year [it was] underfoot in the post office." Other parts of the ritual are forgotten or lost. The lottery is faded and worn out, just like the women's faded dresses and sweaters:
The black box grew shabbier each year: by now it was no longer completely black but splintered badly along one side to show the original wood color, and in some places faded or stained.
Mrs. Hutchinson arrives with her sweater thrown over her shoulders, while the other women have their sweaters fully on. The symbolism here is that the sweaters figuratively represent the callousness and dehumanization produced by living with the annual sacrificial lottery. That Mrs. Hutchinson's is "thrown over her shoulders" signifies that she is beginning to shed the callousness inbred by the lottery; she is turning to a mindset akin to that which dissolved the lottery in "the north village." In light of this, it is painfully ironic that Tessie Hutchinson should draw the fateful black spot.
The final layer of symbolism in the women's clothing is represented by Tessie's apron, and it serves two functions. The first is to symbolically emphasize the mentality that the lottery--as weighty and profound as it is--is an interruption to the workday: "'guess we better get started, get this over with, so's we can go back to work.'" The second is to associate Tessie symbolically with work. In a painful ironic twist, Tessie's association with work is a symbolic association with the work of living which positions her in opposition to the lottery of death. She is kept from joining the lottery early because she is engrossed in her work; therefore, she wipes her hands on her apron because she has been busy living--and without the callousness symbolized by her sweater, which throws on to go to the lottery--instead of busy planning for death.
Mrs. Hutchinson's apron represents the normality of life - she was doing the dishes and "clean forgot what day it was..." The implication there is that Jackson misleads us into thinking that the lottery is important, but that Mrs. Hutchinson was excited to get down to the square. However, normal life happens both before and after the lottery.
The slips of paper are reminicient of a death certificate, to me. The paper represents death, as does the black spot. Black often represents death and the heavy, dark spot, indicates the person to be sacrificed, which is certain death. Black is mentioned also in regards to the black box where the slips of paper are placed - this reminds me of a casket/coffin. It contains death.
Old Man Warner is the old timer - hence the name. He brags that he's lived through so many lotteries and that there's always been a lottery - there's no need or reason to change it, according to him. He's set in his ways.
The village square is discussed as being the place for gatherings - square dances and other things. The village square traditionally (pardon the word choice) is where all important business and fun is conducted. Again, Jackson misleads us with her description of the village square as a beautiful, happy place - and we come to find out that it's a bloody, grotesque place wearing a facade.