In this paper, we study the use of full-duplex radios for continuous feedback of channel state information in MIMO broadcast channels. The simultaneous transmission of feedback on the same frequency band as downlink transmissions causes inter-node interference (INI) at the receiver. We quantify the impact of INI and associated tradeoff in the design of the feedback channel. We show that a continuously adaptive beamforming strategy can achieve higher multiplexing gain with same feedback resources compared to its half-duplex counterpart.