We can add an extra parameter to general relativity (known as the "cosmological constant") to describe "dark energy" observations via a kind of 'anti gravity'; although we still don't fully understand what that means, or whether it's a correct description. It's also unclear whether this would have anything to do with quantum theories (like the standard model).

General relativity can explain "dark matter" observations by assuming there is more mass/matter than we can see (i.e. it's electrically neutral and doesn't interact with light). Since the standard model tries to describe all of the fundamental constituents of matter, and forces including electromagnetism (light), having nothing to say about such a seemingly large amount of stuff is a rather large discrepancy in the standard model.

AFAIK the standard model also says that neutrinos have zero mass; yet we've observed them undergoing radioactive decay ("neutrino oscillation", where each sort of neutrino can decay into the others). Particles which decay require some amount of time to do so. Particles with zero mass always travel at the speed of light (like photons, and hypothetical gravitons) and hence don't experience any time passing (this sentence is a consequence of special relativity). So particles with zero mass can't decay, so neutrinos can't have zero mass. I don't think we've measured their mass very accurately yet; we know it's very small, but it cannot be zero.

[1] https://en.wikipedia.org/wiki/Solar_neutrino_problem

OOPS: I see a sibling comment also covers this. Oh well, I'll keep this one up since it's slightly more eye-catching.