We have a site running Magento 1.8.0 with Varnish 3.0 and Turpentine. It all works great, but for a couple of issues:
1) Selecting "add to cart" on the subcategory page does nothing. Some information on this issue is on these forums https://github.com/nexcess/magento
2) Customer login seems to be sporadic, sometimes not working at all
All of these issues have occurred SINCE installing Varnish and Turpentine. I think some ESI blocks would help.
Looking for a fix ASAP.