How much deviation is acceptable in FFT calculations (using computer algorithms)?
I wouldn't like to give a trivial answer as "it depends on the application" but indeed it does depend on the application! 

Considering the fact that FFT computation will not be the only source of error in many applications it is reasonable to allow some acceptable deviations but generally being bounded by such as the required precision of the overall system.

On the other hand very strict precision bounds may be defined on such as IEEE floating point hardware (or soft simulation) units so that a prescribed set of computations will not generate an error larger than very small epsilon values.

I don't know if such a set of normalized limits exist specificaly for FFT or like algorithms. If you find out that there are mismatches from ideal DFT values and the corresponding fast algorithms you must make your own decision as to whether you should allow this error in favor of some other gains.