This bug also affects disposer methods for application-scoped beans, they aren't called on servlet context shutdown.

There might be a separate issue here that affects not only weld-servlet: Disposer methods for application scoped beans are called after the @Destroyed(ApplicationScoped) event. So the startup/shutdown order is:

@Observes @Initialized(ApplicationScoped)
@Produces @ApplicationScoped // Where necessary
...
@Observes @Destroyed(ApplicationScoped)
@Disposes @ApplicationScoped // Where necessary

This makes it very difficult to have properly scoped startup/shutdown beans interact with each other. A much better order would be:

@Observes @Initialized(ApplicationScoped)
@Produces @ApplicationScoped // Where necessary
...
@Disposes @ApplicationScoped // Where necessary
@Observes @Destroyed(ApplicationScoped)

AFAIK the spec is silent on the order of @Disposes vs. @Destroyed events. The naming of @Destroyed implies that it happens /after/ the context was destroyed, the spec says "fired when the application is destroyed."