We report the experimental study of spectral modulations induced by a stimulated Raman scattering process in an all-fiber all-normal dispersion oscillator. With the use of dispersive Fourier transform, we recorded a series of single-shot spectra of consecutive laser pulses. The data indicate that the Raman process destabilizes the long-wavelength part of the laser pulse spectrum without disrupting the single-pulse generation regime. Our experiments revealed also that the oscillator displayed bistable operation for high pump powers. Two stable dissipative soliton mode-locked states were observed, together with output power hysteresis.