Why is dark-current considered a disadvantage in photo-detectors?
The dark current can be seen as interference source in 2 aspects:


It puts a lower limit on the light intensity you can reliably distinguish from dark current drift
Dark current is connected with reverse breakdown flicker current which you have to filter out to get the useful signal


Both causes come from the same source actually (flicker noise is created by "quick" breakdown current fluctuations which have frequency comparable to your useful signal, and drift represents the slower ones that are easy to filter out if your signal has no constant part). Anyway, the more dark current is, the more interference it creates.