Steps to repro:

Unpack bare Juno JEE.
Install JBDS BYOE feature ("Core Features"). Restart
Install JBDS Branded Product Feature. Restart.
Uninstall JBDS Branded Product Feature (or revert configuration to previous). Restart. Eclipse is now broken:

java.lang.RuntimeException: Application "" could not be found in the registry.

Addtional info:

Bare Juno JEE eclipse.ini:

$➔ cat eclipse/eclipse.ini 
-startup
plugins/org.eclipse.equinox.launcher_1.3.0.v20120522-1813.jar
--launcher.library
plugins/org.eclipse.equinox.launcher.gtk.linux.x86_64_1.1.200.v20120522-1813
-product
org.eclipse.epp.package.jee.product
--launcher.defaultAction
openFile
-showsplash
org.eclipse.platform
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-vmargs
-Dosgi.requiredJavaVersion=1.5
-Dhelp.lucene.tokenizer=standard
-XX:MaxPermSize=256m
-Xms40m
-Xmx512m

or, for Eclipse Platform Binary:

-startup
plugins/org.eclipse.equinox.launcher_1.3.0.v20120522-1813.jar
--launcher.library
plugins/org.eclipse.equinox.launcher.gtk.linux.x86_64_1.1.200.v20120522-1813
-showsplash
org.eclipse.platform
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-vmargs
-Xms40m
-Xmx384m

After installing JBDS BYOE:

$➔ cat eclipse/eclipse.ini 
-startup
plugins/org.eclipse.equinox.launcher_1.3.0.v20120522-1813.jar
--launcher.library
plugins/org.eclipse.equinox.launcher.gtk.linux.x86_64_1.1.200.v20120522-1813
-showsplash
org.eclipse.platform
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-vmargs
-Xms512m
-Xmx1024m
-Djboss.discovery.directory.url=https://devstudio.jboss.com/updates/6.0-staging/devstudio-directory.xml

After installing JBDS branded product, eclipse.ini becomes jbdevstudio.ini:

$➔ cat eclipse/jbdevstudio.ini 
-startup
plugins/org.eclipse.equinox.launcher_1.3.0.v20120522-1813.jar
--launcher.library
plugins/org.eclipse.equinox.launcher.gtk.linux.x86_64_1.1.200.v20120522-1813
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-product
com.jboss.jbds.product.product
-showsplash
platform:/base/plugins/com.jboss.jbds.product
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-vmargs
-Djboss.discovery.directory.url=https://devstudio.jboss.com/updates/6.0-staging/devstudio-directory.xml
-Xms512m
-Xmx1024m
-Dosgi.instance.area.default=@user.home/workspace

After UNINSTALLING JBDS branded product (to drop back to Eclipse + JBDS BYOE), can no longer start Eclipse. Here is the resulting eclipse.ini file:

$➔ cat eclipse/eclipse.ini 
-startup
plugins/org.eclipse.equinox.launcher_1.3.0.v20120522-1813.jar
--launcher.library
plugins/org.eclipse.equinox.launcher.gtk.linux.x86_64_1.1.200.v20120522-1813
-product
com.jboss.jbds.product.product
-showsplash
platform:/base/plugins/com.jboss.jbds.product
--launcher.XXMaxPermSize
256m
--launcher.defaultAction
openFile
-vmargs
-Djboss.discovery.directory.url=https://devstudio.jboss.com/updates/6.0-staging/devstudio-directory.xml
-Xms512m
-Xmx1024m

So, I think we need an instructions.unconfigure in com.jboss.jbds.p2.inf to remove these lines

-product
com.jboss.jbds.product.product
-showsplash
platform:/base/plugins/com.jboss.jbds.product

and replace them with the following when JBDS is uninstalled:

-application 
org.eclipse.ui.ide.workbench
-showsplash
org.eclipse.platform

Also need to know what happens if there are two -product directives... can we just
add (and later remove, when uninstalling) our product to the list, or must we replace
any existing -product entries with ours?