Why does our Solar system not feel the effects of dark matter the way our galaxy does? It is said that stars rotate around the nucleus of our galaxy at too high a speed than should be possible based on the amount of visible matter. An explanation given for this is dark matter. However, the orbits of our planets and other objects in our solar system appear to follow predictable Newtonian/Einsteiniam rules. Why do we not see the same rotational anomaly in our Solar system that we see in the wider galaxy?  
 A: Because the effect is negligible compared to gravitational disturbances from various visible masses in the Solar system, see Does Dark Matter affect the motion of the Solar System? on Science Blogs:

“Let’s calculate it,” the professor said to me, and so we spent the next half-hour doing just that. When we finished, we’d found that about $10^{13}$ kg of dark matter ought to be felt by Earth’s orbit, while around $10^{17}$ kg would be felt by a planet like Neptune. These values are tiny; the Sun has a mass of $2 ✕ 10^{30}$ kg, while values in the $10^{13} – 10^{17}$ kg range are the mass of a single modest asteroid. Someday, we may understand the Solar System well enough that such tiny differences will be detectable, but we’re a good factor of $100,000+$ away from that right now. And that number is only down to around 100,000 now thanks to some new observations, which were egregiously misrepresented by MIT Technology Review. Dark matter is negligible when it comes to Solar System orbits, and it isn’t even close to being detectable.

So why do we detect the effects of dark matter in the motion of galaxies but not in the Solar system? As pointed out in the comments, the difference is scale: effects detectable at the scale of galaxies become too small when scaled down to a single planetary system. For details of calculations see Xu-Siegel's Dark Matter in the Solar System and Constraints on Dark Matter in the Solar System by Pitjev-Pitjeva.
