I don't think that the uniqueness of fingerprints is in doubt, but their analysis and use might not be up to snuff. I've read numerous articles over the last couple of decades that call into question at least the statistical underpinnings of what it means to declare a match.
But law enforcement in general seems to be filled with pseudoscience, from profiling and interview techniques to body language and lie detection.
There was a recent post asking what the self-taught among us feel we are missing from our knowledge base. For me, it's being able to calculate stuff like that for making decisions. I feel like I can spot an equivalence to the travelling salesman problem or to the halting problem a mile away, but anything more subtle is beyond me.
Of course, in this situation, I'd probably just see if I could find a sufficiently large precalculation and just pretend :)