When Jeffreys prior "fails" Context: I am working on a calibration problem involving a 1D function of parameter $\theta$ for which I derived a Jeffreys prior (in fact a 2D but I have an informative prior for one of the parameters).
Observation: Using this prior gives me in practice very bad inference results. Paralelly when using a default choice of the form : $\theta \sim \mathcal{N}(o,1000^2)$ where $o$ is a typical value I get pretty good results. 
Question:
What to do in such a situation (expect checking formulas and code) ? what does it means about my model/data ?
I guess this question is quite abstract but any suggestion or remark would help me.
 A: There's no reason Jeffreys's prior is "supposed" to give you "good" results. The chief motivation behind it is that posterior inferences are invariant to re-parameterization of the model. Is that a major concern for your problem? I can't say. But if it is not, then an alternative choice could improve posterior inferences.
In your case, what these results means is that if you need a more precise posterior that you will need to build a model that accounts for more relevant information about the data generation process, or that includes more information about plausible parameter values. 
Alternatively, you could take the opposite view and conclude that the nonspecific posterior is the most coherent representation of the data, given the set of assumptions you are willing to make, the likelihood, and the data. Then the nonspecific posterior is the just what happens when you have limited information. It's nearly a tautology that having less information implies that you can be less confident that some values are more plausible than others.
