Check out the extended mail action plugin, you can use it the same way you would a standard email but can customize it as much as you would like as well as make use of a large number of variables that can provide additional context in your messages and their subjects:
You won't be able to include things like error messages directly, but there are options such as including a dashboard as a report allowing for things like including an error report filtered on a BT when an incident based around that BT failure rate is triggered.
Is there any detail in particular you're thinking of?
Yep, If I'm thinking correctly about what you're looking for there are variables that can be included any where in the emails using this plugin that can contain information about the agent or host regardless of if you're using an actual agent or even just a monitor.
The actual link there has all of them you can use. We use it as the standard for our email alerts now.