We have investigated the spectral broadening of diode lasers in an external linear cavity with frequency-shifted feedback. With an 850 nm infrared diode of 30 MHz free running bandwidth, we observe a feedback level dependent frequency shift and continuous line broadening up to 5 GHz. A 660 nm visible laser diode exhibits a symmetric broadening enhanced by relaxation oscillations and, at large feedback levels, multimode operation over a bandwidth up to 1 THz, tunable over 3.1 THz (44 angstrom). In each case, the acousto-optic frequency shifter prevents constructive interference of successive roundtrips inside the external cavity and thus the build-up of a discrete axial mode spectrum.