Using a caching server like Varnish is mandatory for running Magento (efficiently). When using extensions that make use of callback API calls make sure that you exclude them from your caching rules.
As we are using Viveum as payment gateway service for most eCommerce projects we generally deploy the official Viveum Magento extension. When using this extension in combination with Varnish make sure that at least exclude the following API calls from your caching list, e.g. through Turpentine URL Blacklist:
ops/payment/ ops/api/
We experienced problems especially related to Paypal transactions without excluding these callbacks, including wrong customer information on the Paypal checkout page.