When a High Availability (HA) environment failed over, on the node that became Secondary, the backup jobs did not gracefully handle the change. The Maintenance Plans are supposed to intelligently determine whether each database is Primary or Secondary in an HA environment, and skip the backup if it is not Primary. This check actually fails (practically speaking) if you have "Verify backup integrity" checked.
Here is a situation I just came across (boiled down and simplified). An end user was having to manually find a user id, navigate to an image folder, and then search through hundreds of images to find the one corresponding with that user. Sure, they were in numerical order, but still, what a pain! He wanted to generate an excel file with links to files to quickly access the corresponding image.
When using AlwaysOn, you must connect using your listener name, not your node name. If you connect with the node name, it will only work until there is a failover, which would defeat the purpose of your High Availability setup, right?