You can add or replace the code in your css on line 2303 –
From this –
.home .entry {
box-shadow: none;
-moz-box-shadow: none;
-webkit-box-shadow: none;
background: none;
}
To this instead –
.home .entry {
box-shadow: 0 3px 6px rgba(0, 0, 0, 0.2);
-moz-box-shadow: 0 3px 6px rgba(0, 0, 0, 0.2);
-webkit-box-shadow: 0 3px 6px rgba(0,0,0, .2);
background: #fff;
padding: 20px;
}
And that will add the white background back for your posts on the homepage. The padding I added will help with the space on the sides as well.
Also, add this to adjust the extra space for the titles on the homepage as well –
.home .entry-title {
padding: 0;
}