Do working physicists consider Newtonian mechanics to be "falsified"? In the comments for the question Falsification in Math vs Science, a dispute around the question of "Have Newtonian Mechanics been falsified?"
That's a bit of a vague question, so attempting to narrow it a bit: 


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*Are any of Newton's three laws considered to be 'falsified theories' by any 'working physicists'?  If so, what evidence do they have that they believe falsifies those three theories?

*If the three laws are still unfalsified, are there any other concepts that form a part of "Newtonian Mechanics" that we consider to be falsified?
 A: One of the problems of Newton's law of universal gravitation, $$F_\text{Grav} = G \frac{m_1m_2}{r^2},$$ is that it does not correctly describe the precession of Mercury's orbit. Mercury behaves slightly different than predicted by Newton's law and general relativity does a better job.
See also the corresponding Wikipedia article.
A: "Falsified" is more philosophical than scientific distinction.
Newton laws have been falsified somehow, but we still use them, since usually they are a good approximation, and are easier to use than relativity or quantum mechanics.
The "action at distance" of Newton potentials has been falsified (finite speed of light...) but again, we use it every day.
So, in practical terms, no, Newton laws are still not falsified, in the sense that are not totally discredited in the scientific community. Classical mechanics is still in the curriculum of all universities, in a form more or less identical that 200 years ago (Before Relativity, quantum mechanics, field theory).
Most concept in physics fit more in the category of "methods" rather than "paradigms", so can be used over and over again. And all current methods and laws fails and give "false" results, when used outside their range of applicability.
The typical example of "falsified" theory is the Ptolemaic system of Sun & planets rotating around the Earth. However, philosopher usually omits the facts that:


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*Ptolemaic system was experimentally pretty good at calculating planet motions

*Most mathematical and experimental methods of the new Heliocentric paradigm are the same of the old Ptolemaic


So the falsification was more on the point of view, rather than in the methods.
A: Newtonian Physics is accurate in the specific domain it was designed for
Physics is not about identifying the "truth" of the world around us.  It's about creating mathematical models that allow us to accurately predict the behavior of the world.
Nobody is trying to create a perfect model, because the complexity of such a model would be infinite.  Instead, we look for the boundaries of a model's accuracy - under what conditions it produces reasonable results, and the precision of the results it produces under those conditions.
You can see this more clearly with other physics models, such as the Ideal Gas Law.  The Ideal Gas Law models a hugely complex system of particle collisions as a simple formula of ratios.  It breaks down relatively quickly at high or low values of any of its quantities, but because we understand when and how the law breaks down, it is still useful.
At extremely large quantities (large speeds, large masses, high energies), the Newtonian model starts to break down, and we need to use a Relativistic model in order to get accurate results.  But that doesn't mean that the Newtonian model is false, it just means that it is inapplicable for those conditions.
Obviously, Newton wasn't aware of the limitations to his laws when he described them.  He was trying to create a universally applicable set of relations.  In that sense you could argue that he failed.  But I would consider the modern understanding a refinement of his laws, rather than a falsification.
A: Relativity is an extension of Newtonian physics, not either a replacement or correction. As such, relativity does not "falsify" Newtonian physics. For velocities far smaller than the speed of light (approaching zero), relativity simplifies back to the Newtonian model. For everyday use, and for everyday engineering problems, Newtonian physics is more than accurate enough. It's only when you get into more "interesting" situations that Newtonian physics fails to provide adequate solutions. The orbit of Mercury is a famous one. It's only because of Mercury's proximity to the Sun that its orbit defies accurate modeling in purely Newtonian terms. Similarly, without an understanding of relativity and relativistic effects on orbiting spacecraft, the GPS system could not work (the onboard timekeeping of the GPS satellites must be extremely precise and the very small relativisitic effects on their clocks must be accounted for). These are not everyday situations, and the relativistic effects are small, but the position of Mercury can be very precisely measured and GPS signals are timed with very high precision (light/radio travels about a foot or about 30cm in a nanosecond).
A: First of all no scientific theory can possibly be falsified. Popper was wrong. See the Quine-Duhem thesis which says that instead of rejecting the theory when a seemingly falsifying experiment occurs, one can always instead reject some underlying "auxiliary hypothesis". The perfect example of this is how when experiments came out seeming to indicate neutrinos were moving faster than light no serious scientists actually believed the neutrinos moved faster than light, rather, all the scientists rightly believed that there must have been something wrong with the experiment.
Now to answer your questions.

  
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*Are any of Newton's three laws considered to be 'falsified theories' by any 'working physicists'? If so, what evidence do they have that they believe falsifies those three theories?
  

Despite what I said above the answer to your question is yes. This is because 'working physicists' are generally not good philosophers of science and many 'working physicists' incorrectly think Poppers program of falsification is correct. Working physicists aren't good philosophers of science because philosophy of science doesn't really help them do their job better and they simply may not find it that interesting, so if they hold misconceptions about philosophy of science it doesn't cause any problem whatsoever in their daily work.


  
*If the three laws are still unfalsified, are there any other concepts that form a part of "Newtonian Mechanics" that we consider to be falsified?
  

No. As I said above no physical theory can be falsified.
Here's some information about Imre Lakatos who has a better philosophy of science in my opinion than Popper.
A: No, they are not considered falsified. They are still a valid low energy approximation, which is all they ever were claimed to be. Or, if you must, they have been falsified at very high energies only.
