Newton's First Law and things that are very old Recently I've been revisiting physics text books, and books by Feynman, and others.
A curious thought has arisen, while I was reading about Mach's principle, and it seems to gnaw on my mind. I hope to have it "rub off" something here.
Consequences of Newton's First Law are:


*

*An object that is at rest will stay at rest unless a force acts upon it.

*An object that is in motion will not change its velocity unless a force acts upon it.


But... this isn't really true in practice is it? Much like we have corrections for relativistic mechanics, when things are going very fast, we should also think about what happens when things go on for a very long time. Eventually, something will happen to the universe, which will impact that object or what we can say of its motion.
EDIT: I worded this last sentence carelessly. What I meant to say is: I can add a correction to the first law, that says the motion stops with a "very very" slow factor, and you would not be able to prove that it doesn't happen. You have not observed things for long enough, or lack the accuracy of instruments to do so.
The way the universe is expanding, or contracting, will ultimately make it so that objects will eventually, not move anymore, or there will at least be some impact as it is moving on. As it were, whatever inertial frame you have will at some point be impacted by an event that makes it non-inertial, inevitably - like black holes, or a total "freeze" of the universe; I don't want to lead with any examples. EDIT: What if this emerges from the corrected law automatically, instead of only being there through interactions between particles?
I know this is a nearly philosophical argument on the difference between theoretical and experimental physics, but in a way, nothing will really go on forever, so any theory that includes this will be too perfect for reality, and does not really model it.
More importantly, I'm wondering if we're not "missing" any minute corrections, carrying over effects from Hubble expansion, or even corrections emerging (no pun intended) from theories on emergent gravity, as corrections to mechanics which could eventually explain some of the discrepancies between the expected growth of the universe and the measured. (https://interestingengineering.com/the-universe-is-expanding-much-faster-than-we-thought)
In any case, is there any research on corrections for things that take a really long time, and how inevitably the universe's maximum age might effect them. Similar to how special relativity ended up adding corrections for speeds (1-lambda)*c, unifying space and time into one fabric where Lorentz transforms are used to compare inertial frames.
Anyway, thanks for reading and for any insights or digressions,
 A: "Much like we have corrections for relativistic mechanics, when things are going very fast, we should also think about what happens when things go on for a very long time. Eventually, something will happen to the universe, which will impact that object or what we can say of its motion."
This is an interesting point but a few things can be said regarding this.  First of all your statement "Eventually, something will happen to the universe, which will impact that object or what we can say of its motion." is made with no proof, it is a speculation on your part but one worth thinking about.  Also, what you state are "consequences of Newtons first law" are actually a statement of the first law.  That confuses me a little.
First of all there is a subtlety in Newton's first law that is not explicitly mentioned, that these motions require a frame of reference against which one measures motion.  Relativistic corrections appear in Newton's second law but the basic laws survive modern physics.  However, the meaning of a frame of reference changes.  In Newtonian physics we often describe Galilean invariance as equivalent to saying that time and space are absolute, and that one can define a universal reference frame.  In relativity each observer carries their own frame and no frame is better than another.  The structure of space-time preserves the speed of light relative to all observes.  In general relativity these frames are locally Cartesian but in the large scale space-time is curved, compressed an stretched by different amounts at different points.  It is well known that "the laws of physics break down in extremely strong gravitational environments", e.g. black holes etc.  So, I'd be more concerned about the law of inertia being meaningless near the big bang rather than the cold dead stage.  
A more fundamental question might be whether or not motion can be defined or have meaning in a universe with just one or two particles.  Since all measurements are based on comparisons and motion relative, and there are no universal frames, it would seem that there is no concept of motion when there are no observers.  What consequence does this have when particles are so far removed from each other that they cannot "observe" each other?  Not sure.  Perhaps over very long periods of time, when the distance between particles becomes infinite, the laws of physics also break down, as in the strong gravitational case.  I compare this in my mind to the old question, If a tree falls in forest and no one is there to hear it does it make a sound?  I would say yes, but this is a different situation.  Here I am saying that if there is no observer, or particle, present the definition of frame may brake down, equivalent to removing the atmosphere for the tree, essential for acoustic to have meaning in the first place!
If you are thinking of the consequences of entropy or possible some universal damping due to interaction with quantum background fluctuations this changes things.  Keep in mind that the laws of mechanics are "classical" laws, even in the relativistic sense.  Quantum mechanics and QFT change the landscape and perhaps one should not assume that these laws are fundamental.  After all, there are quantum corrections to the second law, and only on average do we see these laws obeyed.  This gets us to an even more philosophical point.  We wrote these laws down from a combination of observation and logical reasoning based on what seems reasonable based on our experiences, and we have't experienced everything.  Assuming that the law of inertia is violated one can probably derive some false predictions about the nature of motion that do not match observations (hence it survives by necessity).  The comment about QFT brings us full circle.  While a classical particle far removed form all other particles is not observed by anything, in the quantum world there are always vacuum fluctuations that momentarily create various particle states.  One could argue that no particle is ever really alone.  But considering the true nature of quantum mechanics and field theory matter is not a particle in the first place.  
Before we define laws that govern the behavior of the things we observe we define the things themselves.  The "particle" that obeys any laws, one could argue, does not exists.  It is an abstraction, a mental construct.  The entire discipline of mechanics applies to a non-existent thing, an idealization of an object.  Yet it seems like the more complex feature of bulk matter, compressability, Poisson effect, etc, are explained by building a model of bulk matter made from the idealizations and applying the laws to the pieces of the bulk.  As long as this works we trust the abstraction.  If there is one thing that QM taught us, imo, it's to not hold on too tightly to these abstractions.  They are fictitious.  As long as they work, keep them.  But as soon as they fail, drop them.  
A: 
More importantly, I'm wondering if we're not "missing" any minute
  corrections, carrying over effects from Hubble expansion

I believe what you are trying to get at could be summed up like this:

Since the "motion" of the universe itself is changing, and we measure
  things against that universe, is there not some sort of correction
  that needs to be applied if that "motion" of the universe changes?

Is that roughly it? If so, then the answer is no.
Think about what it means to make a measurement. Any system you can think of would be subject to that same change, and the net effect will be zero. That's, in some ways, one of the corollaries of relativity. You are part of the system, it's you that defines what the scale is, and that will change along with that "underlying real motion".
Take a simpler example. Put a weight on a sheet of rubber. Stretch the rubber. "There!" you say "the velocity of the weight is changing!" But look where you are, you're outside the universe. Such a place does not exist except in toy models. You actually measure things relative to that universe. So let us consider the same toy model but now you measure the speed against a ruler placed on the rubber. Do you see how it will not change? When you stretch the rubber the ruler will also move and the velocity of the weight measured against the in-universe scale is still zero.
Reality tends to be more complex than toy models, but I think you get the idea.
There are, however, effects that can be seen due to this universal motion. These effects require the value being measured to be independent of some local measure. So, for instance, the speed of light is a constant no matter how we care to measure it or what scale we convert it to. c is c in mph and kph. And we definitely see those effects in things like universal redshift - the cosmic background radiation is in the low-energy microwave region, but that's not because it's low energy, it was very high energy indeed when it was released, but in this case we have "moved" in relation to that universal scale, the speed of light, and we see this as a change in frequency - doppler shift due to this universal motion.
