I am using joomla 2.5.28 and virtuemart 2.6.14. I have also tested in a development environment with virtuemart 2.6.16 and the bug exists in both versions.
What is happening is users are not able to delete items from there cart. I am not sure if it is because we use custom fields for all our products, but in any event the customer cannot delete an item once added to their cart. So far, I have only found this bug in IE 11 and older versions.
The odd part is if you engaged the developer tools window the delete button works or if you clear your browser cache delete will work for the current page but if you add new items then delete will now work unless you clear your browser cache again.
I am using jot cache and have disabled caching of the entire cart and confirmed there are no com_virtuemart pages saved in the cache.
Here is a screencapture to demonstrate the issue.
http://screencast.com/t/BaHdKAeUa6
website is references-etc.com
I have no problem deleting products from cart with IE11, tested on sites using VM2.6.14, 2.6.15 and 3.0.6 It seems I have to go through hoops to test order on references-etc.com so have not tried that.
If you go to https://references-etc.com/online-driving-records/order-driving-record-detail and just enter some random driving record data it will bring you straight to the cart.
plus your using a 3rd party checkout and a 3rd party optimisation extension.
BTW could delete the order/product on your site with IE11