Has neutrino redshift been observed? I understand that neutrinos are emitted when supernova explode. I presume that there are quite accurate models that predict the energies of those neutrinos at the time of emission.
Has the phenomenon of redshift been observed when those neutrinos are subsequently detected?
 A: Let's do a Back-of-the-Envelope calculation.
It is typical for large-scale neutrino calorimeters (I have KamLAND specifically in mind because I worked on the project and know the detector reasonably well) to have an energy-scale uncertainty of a couple of percent at a few MeV energy. That's a systematic, and will effect all results more or less equally.
However, that uncertainty comes from the fitting uncertainty to the calibration data which shows broader peaks than that (we use a bunch of peaks to help). The breadth of those individual peaks gives you an idea of the event-to-event random uncertainty.
For argument's sake let use an optimistic $\sigma_\text{event} = 0.05\,E$ as the random uncertainty of a single event with true energy $E$. The uncertainty on the position of a peak goes by the square-root of the number of events in the peak.
$$ \sigma_\text{peak} = \frac{\sigma_\text{event}}{\sqrt{N}} = \frac{0.05}{\sqrt{N}} E\,.$$
That's the number that you have to get down to the energy difference that you want to detect, and that is going to be hard.
Assuming the original energy of the source is known exactly, to measure a 1% red-shift you need 25+ event from that source. To measure a 0.1% red-shift you 2500+ event. To measure a 0.01% red-shift you need 250,000 events....
You need a a lot of events from a modest energy source that has been heavily red-shifted.
A: Neutrinos are notoriously difficult to detect . Have a look at this review paper : 

A core-collapse supernova will produce an enormous burst of neutrinos of all flavors in the few-tens-of-MeV range. Measurement of the flavor, time and energy structure of a nearby core-collapse neutrino burst will yield answers to many physics and astrophysics questions. The neutrinos left over from past cosmic supernovae are also observable, and their detection will improve knowledge of core collapse rates and average neutrino emission. This review describes experimental techniques for detection of core-collapse neutrinos, as well as the sensitivities of current and future detectors. 

In page 13 of the pdf file there is a table with the experimental data base of detected neutrinos from supernovae the statistics are such that detailed fits to estimated spectra will have large errors. Possibly in the future experiments some discrimination could be obtained to be able to bound the redshift , either from the gravitational field of the supernova or the  redshift from the relative motions. It would all depend on modelling of course. One can measure red shifts for photons from displaced spectra of atoms, but it is not possible to do that with neutrinos. Maybe the two body Kaon and pion decays  at the explosion with a proper modelling might give some indications in the future, but I doubt it. 
