Backups can be used to access the sensitive information saved in the file system (check the initial point of this checklist)
Also, backups can be used to modify some configurations of the application, then restore the backup on the phone, and the as the modified configuration is loaded some (security) functionality may be bypassed
Check if the application is registering any protocol/scheme
Check if the application is registering to use any protocol/scheme
Check if the application expects to receive any kind of sensitive information from the custom scheme that can be intercepted by the another application registering the same scheme
Check if the application isn't checking and sanitizing users input via the custom scheme and some vulnerability can be exploited
Check if the application exposes any sensitive action that can be called from anywhere via the custom scheme