Debugging ​
Since all logic runs in ABAP, you can debug everything in the ABAP environment. Set an external breakpoint, because abap2UI5 apps are called externally via HTTP.
Backend ​
Set a breakpoint in your abap2UI5 app to debug the code. Check that the XML view builds correctly and that all events fire on the backend as expected.
Frontend ​
On the frontend, abap2UI5 behaves like a standard UI5 app, so the usual tools and debugging features work.
Developer Tools ​
Press Ctrl+F12 to open the built-in Developer Tools of abap2UI5:
Six tabs cover the whole roundtrip: Overview, Problems, Roundtrips (each request and its response), View & Data (the rendered XML and the model of the slot you pick — main, popup, popover, nested), System and Search.
The footer offers Retry, Restart, Logout, a jump to ADT, Copy, Report a Bug and an Export that bundles everything — including the running app's ABAP class source — into one blob you can attach to a bug report. Error popups also carry a copy-to-clipboard button for the same purpose.
UI5 Inspector ​
Another option: the SAP default debugging tool, the UI5 Inspector.
Issues ​
If your code looks correct but you suspect a bug in the abap2UI5 framework, build a minimal sample that reproduces the bug and open an issue on the abap2UI5 repository — we'll investigate and fix it.