Are there any (known) violations of Newton's First Law? The way I have seen in presented, Newton's First Law is an empirical observation. Therefore, it seems plausible that it is not true in all cases. Have there been any attempts to seek out violations and/or is there some reason no attempts have been made?
 A: Newton's first law is most commonly violated in non-inertial reference frames. Often, rather than considering the law to be an empirical observation, people instead consider it to be the definition of an inertial frame.
A: Principles in Physics are not always a compact summary of direct experiments. It is perfectly valid to introduce as a principle (law) some statement not directly amenable to direct measurements but such that its consequences are.
It is enough to think of the case of Maxwell's equations, the laws of electromagnetism. Nobody checks or has checked them by measuring directly the $div$ or the $curl$ of vector fields but rather by extracting the measurable consequences of the equations for the fields on the motion of charged particles.
In a similar way, the validity (or violation) of Newton's laws as principles of dynamics is verified every time we compare predictions about the motion from knowledge of forces and initial conditions and experimental values of real motions.
Newton's laws have no unconstrained validity. Each of them, in a sense, is violated in specific conditions. However, in order to identify the cases of violation, one needs to start with an explicit statement of each law. This is an important step because there is more than one version of "Newton's laws."
In particular, with reference to the First Law,

*

*if it is stated as Newton did as a body on which no net force is acting moves uniformly, we need to clarify what definition of force we are using. If we state that forces are only due to interactions with other bodies, @Dale's example is enough.

*if it is stated (as in Landau&Lifshitz textbook on Mechanics) as a statement about homogeneity and isotropy of the configuration space of an isolated body, we need to verify such symmetries;

*if it is stated as a claim on the existence of special reference systems, we have to characterize them, and we need to verify, on the basis of measurements, how inertial is a specific reference frame.

It should be evident that the final answer to the original question depends on the exact wording of the First Law.
A: Scientific explanations operate, roughly, in two separate levels of understanding: the framework and the model.
Newton's first two laws are best understood as trying to provide an explanatory framework. Frameworks are the playgrounds in which models play. Without phrasing a model within a framework, that framework makes no predictions about the world. In turn the explanatory framework is compatible with all manner of observations, and cannot be disproved by observation.
Newton's explanatory framework is, roughly, to say “In the past, it seemed obvious that whenever something was moving there was a force which explained its motion, and you might therefore have defined $\sum_i F_i = mv$ or so. However after the work of Galileo it seems like a ball set in motion will roll across a level floor indefinitely, and I choose not to explain this tendency in terms of a ‘force’ anymore, but just take it as the natural state from which all deviations must be explained. Instead of a force being a disposition to move, I define a force as a disposition to accelerate, $\sum_i F_i = m~ \mathrm dv/\mathrm dt.$ When things are moving with a constant speed in a straight line, that requires no explanation other than the forces are balanced, when things deviate from the straight line that is where we speak of forces causing them to deviate.”
Now, what falsifies an explanatory framework like this? That is more subtle. Frameworks get falsified, as they get clumsier to use. So for example, one thing that would have made this very hard to use is if you could not use vector summation to analyze multiple forces acting on a single particle. The two laws would not care: you would say that “you have force A, and force B, but oh, whenever you have both of those forces there is the nonlinear coupling force AB which must also be considered in the resulting sum.” But in practice this would be very tedious to work with and people would try to find a simpler way to describe the world.
Or, let's take the things that actually falsified it. Quantum mechanics, to start: the above framework says you should understand the phenomenon of Heisenberg uncertainty as “as you confine a particle to a smaller and smaller box it increasingly feels a random-looking interaction with whatever box-walls-forces you are imposing. However do not be fooled as the interaction seems to have many correlations with a global-hidden-variable reality which prevents it, for example, from violating conservation of energy in the long run, even as over short times we find particles escaping their potential wells that should have confined them.”
Heisenberg chose to try and preserve Newton's laws by instead promoting all of these vector components—force in the x direction, momentum in the y direction, x-coordinate of position, etc.—to be matrices over an unknown vector space using complex numbers. This allowed him to understand Heisenberg uncertainty as $x~p_x\ne p_x ~x$, for the usual real numbers order does not matter, but for these physical observables maybe it does.  He made a very good attempt! We still use it to understand real systems, it is a working restatement of the core of the Schrödinger equation. But you can see in $x~p_x\ne p_x ~x$ the sort of thing which eventually falsified Newton’s first two laws. (That and special relativity.)
