Dale said:
It doesn’t predict gravitational time dilation or the correct light deflection or the precession of Mercury or the Shapiro effect or frame dragging.
MOND isn't meant to do any of those things. It is unabashedly and has been from the start, a toy model. The reason that it is described as modifying Newtonian dynamics, rather than modifying general relativity itself, is that in weak fields at galactic scales, Newtonian gravity is an excellent approximation of general relativity. Mordehai a.k.a. Moti, Milgrom, who invented MOND was perfectly familiar with GR (and indeed basically a GR physicist) and knew that a non-toy model version of MOND that perfectly described reality would have to be a general relativistic generalization of MOND (a mathematically consistent generalization called TeVeS was devised by Bekenstein, but as it turns out, that particular generalization doesn't describe what is observed in certain respects, so it is the wrong generalization) and might deserve a new name (e.g. MORD for Modified Relativistic Dynamics).
The domain of applicability of pure, toy model MOND, is limited to weak fields in circumstances where GR is well approximated by Newtonian gravity, to the point where post-Newtonian GR effects are too small to measure, and where Newtonian gravity is used in practice by astronomers as a result because the math is much, much easier with no consequences that aren't much smaller than their observational measurement error (it turns out that lots of astronomy measurements at the galactic scale actually have pretty big error margins relative to experimental measurements in other parts of fundamental physics; the MOND acceleration constant, for example, is known only to about 1% accuracy).
But, the concept of modified gravity is that you really start with GR or quantum gravity theory that approximates GR in the classical limit, and then tweak the extremely weak field behavior of that gravitational theory in such a way that it gives rise to a transition from the effectively almost perfectly Newtonian gravitational regime to the MOND behavior gravitational regime when the gravitational field gets weaker than the critical field strength that is the single fixed parameter in MOND.
While in its domain of applicability we describe that transition point as a transition from the Newtonian regime to the MOND regime, what everyone who uses it understands is that what is called the "Newtonian regime" is really just plain vanilla GR, and that the MOND regime is simply used to determine the magnitude of the gravitational field strength at a particular location, understanding that it will deflect light at that point in the same way that a field of that strength in conventional GR would.
So, while it is called modified "Newtonian' dynamics, at local scales MOND is actually, definitionally, conventional, unmodified general relativity, which we know holds true with exceptional precision, even thought we don't know precisely how to put MOND effects into the GR equations in fields that are weaker than the cutoff acceleration value.
By analogy, at velocities much smaller than the speed of light, we neglect the effects of special relativity because they are so tiny that they aren't measurable, just as in the situations where MOND is applied, the effects of general relativity relative to Newtonian gravity are so tiny that they aren't measurable for gravitational field strengths of slightly more than the acceleration constant of MOND at which MOND effects kick in. But, just as engineers who neglect special relativistic effects when modeling aerodynamics for an airplane design don't in any way presume to be saying that special relativistic effects aren't part of the laws of Nature, astronomers who apply MOND without considering the GR effects that you mention (other than the deflection of light) don't in any way presume to be saying that gravity outside the MOND regime is actually Newtonian rather than general relativistic.
What is probably going on is that MOND arises from some sort of second order quantum gravity effect in which the strength of the second order effect gets smaller with distance at an exponentially slower rate than the first order gravitational effect described by GR and approximated by Newtonian gravity, but with the second order effect multiplied by some very small constant, such that the second order effect isn't close in magnitude to the first order effect, until you reach the MOND cutoff acceleration. So, in gravitational fields stronger than the MOND cutoff, the first order effect is much stronger than the second order effect, and in gravitational fields weaker than the MOND cutoff acceleration, the second order MOND effect is very swiftly much stronger than the first order gravitational effect described exactly by GR and approximately by Newtonian gravity, as the first order effect gets weaker with distance much more rapidly than the MOND effect does.
The one way that MOND toy models differ from each other (discussed in Milgrom's papers on the topic back in the 1980s) is in the interpolation function used to transition from the "Newtonian" (actually conventional GR) regime to the MOND regimes. Many of these interpolation functions, by design, reflect this kind of understanding of what is going on.
The bottom line of all of this is that above the MOND acceleration cutoff, MOND is understood by everyone who uses it to actually be conventional GR, despite the name. So, there is no failure of MOND at local scales.
In particular, since the gravitational field of the Sun is stronger everywhere in the solar system than the MOND acceleration constant, there are no solar system effects of MOND, which is simply exactly equal to GR in the solar system.
Dark matter particle theories likewise predict that it is indistinguishable from GR without dark matter at solar system scales with existing levels of observational precision, because the amount of dark matter in that volume of space is so small and because that dark matter is so evenly spread out within the solar system.
