Frequency dependent phase difference between signals arriving at two microphones I wish to calculate the time difference between a signal (may or may not be periodic), arriving at the right and left channel of a stereo microphone pair kept at a distance of about 30 cm. I am doing so to localize the acoustic source.

I compute the FFT of the left channel and the right channel, and then find the values of the FFT at a particular frequency bin of interest. I then divide the (complex) values to get the phase difference in radians. I then convert the phase difference to a time difference ( time difference = phase difference / 2* pi ) and use this to calculate the angle of arrival of the acoustic source.  

What are the ambiguities that could occur in this method of calculating the time difference, as compared to a cross-correlation method of finding time difference?

I am using this method rather than cross-correlation due to the frequency dependence of the phase difference.
For a constant time difference, the unwrapped phase difference measured at the centers of the two windows is linearly related to frequency. (To measure phase at the center of an FFT window, use an fftshift prior to the FFT, or flip the phase of the odd numbered FFT result bins.)  So you can use all of the FFT results, not just one bin.   The low frequency bins may help in determining the potentially ambiguous phase unwrapping of the higher frequency bins, if the signal is sufficiently wideband.