From what I have read, FFT seems to simply be faster than DFT, thus making DFT redundant. However, if computational speed is not an issue, are there any advantages of using DFT over FFT (such as increased precision, for example)?
The conventional FFT algorithms are only "fast" if the number of data points can be factorized completely into small integers. (That is less restrictive than the first FFT algorithms, where the number of data points had to be a power of 2).
A DFT may be faster if you only want a small number of Fourier coefficients from a large number of data points.
I wouldn't expect precision to be an issue either way, though I haven't investigated that in any detail.