@jamepompey: Theme is responsive but the your table in homepage is not responsive. It has lot of columns in table so it doesn’t fit. Can you try using Responsive Table plugin or responsive columns plugin and add in.
Same with your product page, where your details has fixed width of 525px. So, it’s issue. That can be fixed by adding in max-width css. Just add the following css in “Appearance => Theme Options => Custom CSS”
.single-product .product_info { max-width: 100%; }