  Superresolution techniques based on intensity measurements after a spatial
mode decomposition can overcome the precision of diffraction-limited direct
imaging. However, realistic measurement devices always introduce finite
crosstalk in any such mode decomposition. Here, we show that any nonzero
crosstalk leads to a breakdown of superresolution when the number $N$ of
detected photons is large. Combining statistical and analytical tools, we
obtain the scaling of the precision limits for weak, generic crosstalk from a
device-independent model as a function of the crosstalk probability and $N$.
The scaling of the smallest distance that can be distinguished from noise
changes from $N^{-1/2}$ for an ideal measurement to $N^{-1/4}$ in the presence
of crosstalk.
