I reproduced the problem using pure ITK (the version that is used by Slicer).
The repo to reproduce the problem is here: https://github.com/fedorov/itk-gdcm-dcmtk-readers
GDCM reader fails with the same error as in Slicer:
Exception thrown while reading the series
itk::ExceptionObject (0x7ff2538696d8)
Location: "virtual void itk::ImageBase<3>::ComputeIndexToPhysicalPointMatrices() [VImageDimension = 3]"
File: /Users/fedorov/local/builds/Slicer4-Release/ITKv4/Modules/Core/Common/include/itkImageBase.hxx
Line: 187
Description: itk::ERROR: Image(0x7ff253873c90): A spacing of 0 is not allowed: Spacing is [0.3125, 0.3125, 0]
DCMTK reader works just fine, and results in a volume with slice thickness 1.3, as expected.
I will follow up with the ITK folks, but this experience, once again, begs the question - why do we rely in ITK and Slicer on GDCM and not on DCMTK?