First of all, Conga Composer is a great document generation tool on the Salesforce.com platform. Probably the best, in my opinion. But it does have some odd issues, like everything in the world. The most odd one is this issue of not able to accommodate two entry points in the same browser session. So if you try to run Conga off both your production org and a sandbox org, which is quite common for a developer/admin, it totally gets confused and becomes unable to retrieve templates. You might see "No Templates available" on the template selection screen, and an odd error like "can't open E:\templates\v0000010345" when actually trying to merge.
Fortunately I usually have different browsers open for different orgs, so that's not an issue for me. I only noticed it once when I was trying to test IE compatibility for multiple orgs. It looks odd because you'd think the transactions should always be identified by SFDC session IDs and instance endpoints, which has nothing to do with the client launch point. Besides, exposing the server info in error messages is never a good idea. :)