> Rather like the way light can appear to be either particles or waves depending on how you measure it?
No. As in we literally get different answers depending on the method used.
One method of measuring distances is to use objects in other galaxies that have a known brightness, like a specific type of star or supernova. By comparing the observed brightness to what we know it should be, we can determine how far away it is. Combine that with a phenomena called red shift (the doppler effect applied to electromagnetic waves due to the universe expanding) and we calculate the rate of expansion of the universe.
The other method is to use the cosmic microwave background. We have a detailed "map" of the early universe's structure, and we can use that to mathematically model and calculate what the structure of the universe should look like. We refine the model to make it match the universe as we actually see it. That model includes how fast the universe is expanding, so that's one of the things we indirectly measure using this method.
As of about ten years ago, these two methods gave essentially the same result. As our methods improved, however, the results started to diverge... and now it's at the point where the difference between the results as so different they can't be explained by errors in measurements alone. The harder we try to check and verify either method, the more confident we are that either method is correct, but the more divergent the results become.
This means something, somewhere, is wrong. Nobody knows what it is yet, but there's a lot of things to verify and some theories to test yet.
=Smidge=