We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well as a highly-unstable supercontinuum regime spanning an octave in bandwidth. Wavelength correlation maps allow interactions between separated spectral components to be identified, even when such interactions are not apparent in shot-to-shot or average measurements. Experimental results are interpreted using numerical simulations. Our results show the clear advantages of dispersive Fourier transformation for studying spectral noise during supercontinuum generation.