Experimental proof for Conservation of Total Energy 
In physics, the law conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time.
  (Source : wikipedia(conservation of energy)

And

Truly isolated systems cannot exist in nature, other than allegedly the universe itself, and they are thus hypothetical concepts only.
  (Source : wikipedia (isolated system)

Clearly depict a loophole in the law of conservation of energy as the law holds in case of isolated systems and apparently these do not exist.
I thought of various practical experiments to inspect the actuality of the law, but in reality I could not think of a single experiment which does not send off energy in form of heat/sound/light out of the system. Even the experiments performed in UCLA here states that some energy will be uncaccounted for in the experiment !
Even a simple experiment of a ball falling down creates heat from friction with air. Clearly the law must hold if we conduct the entire experiment in an isolated system, but these simply do not exist.
Magnetic levitation to experiment with conservation of energy experiment is not an option as the levitation requires energy and going back to source, we come up with the same heat release problem which makes this experiment only a complex version of the first one.
Note : I am not talking about approximations
Since we can not make any sort of isolated system without it leaking/absorbing energy into the surroundings. The discussion of the conservation of energy boils down to the conservation of energy of the entire universe.
Through various texts I came to the conclusion that the total energy of Universe is not a constant. Those texts being (1, 2, 3)
Even the ArxiV paper listed as 3 states only

Despite remaining hesitations about where additional mass could be coming from, on the overall balance of consistency, we conclude that the energy conservation law is better obeyed by means of increasing mass of the universe with its radius
  Conserves only a type of energy as it suggests increment in mass which is also a type of energy.

I believe this looks extremely like challenging the law of conservation of energy which is supported by neother's theorem among many others. But I just wish to determine whether practically this law is actually valid or not !
I do not expect to get answers of 99.99% conservation with the negligible heat being lost neglected.
I understand that GR does not say energy is conserved but the scales of day to day life and that of GR are different which makes energy conservation at earthly scales even if 99.99% a boon. But this just means that energy conservation depends on the working scale and experiment and ranges from nearly 100% in some to not conserved in various aspects of GR.
Finally the bottom line of question is, can we experimentally prove that energy, total energy is actually conserved ?
(a Yes answer requires a detailed experiment with complete conservation and no loopholes)
 A: 
Finally the bottom line of question is, can we experimentally prove that energy, total energy is actually conserved ?
  (a Yes answer requires a detailed experiment with complete conservation and no loopholes)

Elementary particle physicists have been doing this for more than sixty years. Conservation of energy is one of the main constraints that built up the standard model of particle physics.
We have first to agree about "proof". In my above assertion I consider it a "proof" that the law has not been falsified by any of the data used to discover the great symmetries of nature in the standard model. And the number of experiments and events in the experiments are way over the five sigma deviation for statistical proof.
We also have to agree that for any measurement in the real world there will be errors, and all the values measured are accompanied by a +/-  of the error of the measurement.
Energy conservation is, within errors, always true in decays. Look at these decays in the bubble chamber of  a lambda and an antilambda:


Caption: Bubble chamber photo of the production & decay of a lambda particle & its antimatter equivalent, an antilambda. The particles are produced from the annihilation of an antiproton which enters the picture at bottom. Being neutral, these lambda & antilambda leave no tracks, but they reveal their presence by decaying into charged particles which form V-shaped pairs of tracks. The two "vees" near the bottom of the picture are produced by the antilambda (left) & the lambda. The antilambda decays into an antiproton (left) & a positive pion, the lambda into a proton (left) & a negative pion. 

We can measure the momenta of the decay products, with the experimental errors, we can identify the proton(anti) and the pi-(+) by the ionization they leave in the bubble chamber . We have done this in a huge number of experiments and measured  the mass of the lamda as  
1115.683±0.006 MeV/c**2 
It all comes because in elementary particle interactions four momentum is conserved . Fitting interactions with the constraint of four momenta conservation has built up for us the particles and resonances that fit so beautifully into the group representations of the standard model. 
A: No, we cannot prove that energy is perfectly conserved experimentally.
The first problem is that you would have to run an uncountably infinite number of experiments to "prove" that conservation of energy is true. In some hypothetical universe, you might run one trillion experiments where you calculate the energy of, say, a falling ball as well as the energy it imparts to the air on its fall. In this wonderful universe, these two things add up to exactly 100% with no decimals. What if when you hold your tongue out 45 degrees to the left, the ball falls faster or some other ridiculous thing? So, from a philosophical stance, it's not possible to prove any scientific hypothesis/theory/law perfectly. You can "prove" it beyond reasonable doubt, but not perfectly.
A second problem is that of accuracy and precision. Where should we get a machine that measures energy (or some value from which energy can be calculated) to an infinite number of decimal places? You're saying that accounting for 99.99% of the energy is insufficient. I assume that accounting for 99.99999999999% of the energy would also be insufficient? In that case we would need some kind of perfect instrument that could never exist in our universe (so far as we know).
A third problem: ∆E∆t >= hbar/2. Our current understanding of the universe indicates that even if we somehow had perfect equipment, energy can never be measured perfectly. Essentially, the uncertainty in energy multiplied by the uncertainty in time can never be less than hbar/2.
So, what does that all mean? Ultimately, all of science (and therefore physics) is our current best guess. To say that something is absolutely proven beyond any possible doubt is to say that we are no longer open to new information. This goes against everything that science stands for. But does this mean that we're shooting in the dark? Did some crazy person just guess that energy is conserved and we all went with it?
Not quite.
There have been probably hundreds of thousands or millions of measurements of the conservation of energy. Of those many measurements, no set of measurements that disagrees with conservation of energy has ever stood up to serious scrutiny. In science, when we make a measurement we need to also look at the uncertainty in the measurement. Perhaps we have a system where we can measure both the before and after energy of an object, as well as the heat and sound generated by it. We add up all the before energies and all the after energies to find the before is 10 J, and the after is 9.9 J. There. Conservation disproven? The experiment, and any instruments used in it will have some uncertainty. What we should really write is before = 10.0 ± 0.2 J and after = 9.9 ± 0.1 J. Since they agree to within experimental error, all we can say is that conservation does not appear to be violated.
Unfortunately, that's the reality. No measurement can ever be exact. If you think that only accounting for 99.99999% of the energy in a system means that energy isn't actually conserved... there's a small (so small as to be virtually indistinguishable from zero) chance you could be right! In science though, we have to eventually accept certain things as true in order to move on. In a perfect world, every scientist would verify every principle for themselves from first principles. But if that were the case, we would all still be tossing rocks in the air and timing how long it takes them to fall. Perhaps the best argument that conservation of energy works is that planes stay in the air, phones connect to the internet, and the sun rises every morning. It would be amazing if one of the core tenets of physics was found to be extremely incorrect and yet all these things that we've based our physics on actually work.
No physicist can ever impart absolute truth to you. We leave that up to the mathematicians.
A: 1) Homogeneity of time throughout the universe (electronic transitions of atoms and molecules, then telescopes and spectroscopy). 
2) Noether's theorems. 
3) Mass-energy is conserved.
However, (1) is not exactly true locally.  We live at the bottom of a gravitational potential well.  GPS demonstrates that time passes faster when residing higher in that well. General Relativity lacks conservation laws.  Magnitude matters!  Given the uncontested loophole in Noether, exploit it.
