Make sure you have the notifications turned on for the particular thread, blog or forum you want to receive notifications on.
For example in Members blogs (/members-area/b/blog) you'll see the actions on the left hand side:
You can then click to turn blog notifications on, you can also bookmark the blog application. This should tell you when new blogs are posted to this application area, but not necessarily to the whole group as there may be other blog applications in this group.
If you only want notifications about a particular blog, click through to the blog and under the 'more' menu you will see:
Here you can turn comment notifications on for the blog, even if you didn't create it, and notifications for the blog application it resides in.
Documents have a similar option under 'Actions' but these options aren't hidden under a 'more' link:
Basically keep an eye out for 'more' links and 'action' widget sections.