How can I track stale content and alert content owners to it?
It's been awhile since you asked and I'm assuming you found an answer. For those who come across this post, the Rules module should handle this requirement. 


Create a rule to react when content is viewed, which should suffice as a trigger. 
Add a condition to run a data comparison on node modification date or write custom PHP comparison code.
Set the rule to send an email to the node's author.