Is the discrepancy between quantum mechanics and relativity only in the math involved or is it much deeper? That is, do the same interactions have different and non-comparable interpretations in both, or are the mathematical equations involved wrong with respect to each other?
What are some examples of this discrepancy?
How far along are we from an unified theory?
The unified theory of particle physics, $\operatorname{SU}(3)\times \operatorname{SU}(2) \times \operatorname{U}(1)$, uses Klein Gordon and Dirac and quantized maxwell equations to solve for quantum mechanical systems, and at a meta level quantum field theory. All these are 100% compatible with special relativity.
If by relativity you mean General Relativity, GR, , i.e. quantization of gravity, yes , GR is not quantized definitively yet, i.e. there is no standard model. String theories have quantized gravity and unify it with the standard model of particle physics but there still is no definite model which can be tested for validity, as there are too many of them.
The discrepancy with the standard model is in the math involved , because GR is a deterministic classical theory, whereas the standard model of particle physics is based on quantum mechanics and probabilities.
