The current options for the inbox are:
A third tab should be created which only shows tasks where someone has tagged you via “@”. In our business, we have found that when someone is tagging you, it is typically a more time-sensitive task. It would allow for better productivity if we can address these tasks without having to trawl through the entire activity feed to find them.
Other suggestions would be a way to allow you to filter/ sort the inbox (tagged items first, followed by date order second etc).
Another would be a way to create your own filters for notifications that run across the top of the inbox. It would be like creating a custom report.
I would love to hear what other people think