To say that "Newton's law of gravitation has been falsified." Not very useful at all. Most scientist know that they dont know everything. At least that was the way I was taught and the conclusion all my classmates came up with.

To say something is 'falsified' does not mean it is useless and should be tossed. Newtonian dynamics is virtually dead on for everything we can measure that doesnt involve a close approach to a stellar mass. As a side note, there should have been anomalous changes in sun grazing comets also. When you combine all the data, it shows that there is some effect due to mass on how orbits are shaped. Oddly enough, then someone put that bit of data into a theory, added in SR, and POOF, we had a pretty good explanation of the anomaly.

Dark Matter is the same in many ways. First, like I have said here many times, the name Dark Matter is a placeholder showing that we dont have the slightest clue as to what it is. Now we call it cold, or warm or hot dark matter, because we have an idea from its behavoir as to the internal energy of whatever DM is. The thing is tho, that we still dont have the slightest clue what DM actually is. So, to say "predictions from computer models fail to live up to the realty provided by observations" is kinda pointless. We dont know how good the model is, because to some degree the model is a guess as to all the properties and distribution of DM.

The thing is, even if we do get a pretty good idea of what DM is, that dosent mean the theory is perfect. Going back to the GR example, we still havent detected gravity waves directly. Should the current or next generation of detectors not find any, then GR will have a problem. Either the calculated intensity of the waves is off, or mayber there is something that damps them in space, or maybe our understanding of the experiment is bad. That doesnt mean we toss GR by the wayside any more than we tossed Newtonian dynamics. It only means that a new theory will need to be made that explains things better.