I know this is very old, but same thing just started happening to me.
In the Debugger on the right under 'Breakpoints' it said 'No breakpoints', but as the page loaded it kept breaking at a particular line, and the page wouldn't finish without me manually stepping through a load of stuff.
If I then added a breakpoint on that line (as suggested above) it added it to the list of breakpoints on the right as expected, but weirdly a second breakpoint (for a different line) magically appeared in the list of breakpoints as well, which seemed a bit buggy. Removing either/both didn't stop the problem.
On closer inspection of my code I realised I'd messed up commenting around that line (using a clumsy mix of /**/ and //) and that was causing the debugger to kick-in and break execution. I haven't seen mistakes in code do this before - I normally just get an error in the console, but the page finishes. Maybe something about errors in comment tags triggers the debugger?
Anyway, thought I'd share in case it's useful for someone else.