bdc does not exist

This error message can occur when you are configuring an external content type profile page host in the BCS service application. Of course the most likely cause is that you neglected to create a profile page host site. All you need is a site somewhere in the farm based on the "blank site" site template.

But there is another trap for people setting up multiple farms with federated service applications. If you fedarate the BCS service you end up with two places that you can get to the Business Connectivity service application management page. You can get to it from Central Administration on the hosting farm, or you can also get to it from Central Adminstration on the consuming farm. Presumably you will want to create the profile page host on your consuming farm. If you go to the management page on the consuming farm you will be fine. If you use the management page on the hosting farm you will get this error, because the hosting farm doesn't know about the consuming farm's web applications. If you didn't know that you could spend a long time trying to get the profile page host site URL right. Oh dear.