Yes upcycling is an often forgotten option for things like broken electronics and worn out clothing... connecting the general public to niche communities like local maker/hacker spaces, artists/crafters, teachers/schools in need of materials even, would be great - I know there is a market for all kinds of scrap material - often it's just a matter of making people aware this need exists and making them easy to find.
Perhaps for those things that cannot be recycled, it might be good at that stage to provide a few resources on what else can be done with it? Of course this will vary by region - at the worldwide or national level, it could simply link to general references such as http://freecycle.org, or retail chains that accept certain materials - locally would open up other possibilities. For instance here in Chicago there are places that take large items like building materials - the city provides alternate suggestions on its website as well (http://www.cityofchicago.org/city/en/depts/streets/supp_info/recycling1/recylingaz/lettera1.html) which would be a great feature to have in this app, whether it integrates with existing resources, or maybe can incorporate user contributions?
Regarding the idea of the loyalty app - I wonder if something like Foursquare might be employed for this purpose, in which people could be engaged and encouraged through the app, and rewarded by the business for bringing in recyclables? Customers could "check in"/get a stamp every time they bring back recyclables, and after a certain number of these, be rewarded with whatever the businesses chooses?