We made did a campus LAN upgrade recently, during which we migrated from a mixed EIGRP/OSPF IGP to a multi-area OSPF redistributing to/from BGP on our WAN. We have two entry points on different sides of the campus with two different AS' numbers, so not running iBGP. We accidentally introduced asymmetric routing to our WAN, which we bandaided with static routes. We're working on changing the routing - using the same AS and running iBGP between the two routers to the WAN, sending community strings changing the provider's local pref, etc.
Question is: Why did the asymmetric routing - going out router1, coming back router2 - why did it matter to the applications? How do the applications know there's asymmetric routing? What immediately broke for us was XEN desktops, and Microsoft Remote Desktop. I can understand how the network would be able to tell with something like URPF, but why does it matter to applications and how do they know?