I've been seeing this error more and more recently, both inside and outside the walls of my employers. The Directory Links across partitions are not allowed error seems to routinely crop up when you have created an OData source with Visual Studio and have uploaded the model to the BDC in SharePoint. What seems to be happening then is you create a new content source in Search for the BDC and configure it to crawl all BDC applications. Then whenever you do a crawl on that content source you get the error message described above.
I was fortunate enough to have Venkatesh work with me on this a bit and what we found is that if you change the content source to crawl the individual BDC applications instead of the entire catalog, the error went away. For illustration purposes, here's what this configuration looks like in the content source UI:
This should get you to the point where your crawls are able to complete successfully and you can find content when executing a query. After that, things get a little more dicey…in all honesty right now the links for BDC search results don't really appear to do anything useful, but that will be the next lump of coal I dig into. Meanwhile, I know lots of people have been hitting this error so I wanted to share this while I have it, and then continue to flesh it out as we make progress.