There are a couple of quibbles that can easily be addressed.
The LTV talks explicitly about price, not use-value. A commodity that takes twice as much labor to produce as another is not necessarily twice as useful or inherently valuable the other commodity. The LTV says only that if some item is actually traded for some other item (i.e. presuming the use-value of the items justifies the trade, and therefore makes them commodities), the relative magnitude of the trade will be determined by the amount of labor necessary to produce the items. If it's worth trading hats for shoes, and it takes twice as long to make a pair of shoes as to make a hat, then one pair of shoes will be traded for two hats.
All the quantities in the LTV are not individual but statistical quantities, and they are all relative to the physical means of production actually in use. "The amount of labor necessary to produce a commodity" is a statistical property of how much labor is necessary to produce all the shoes in a particular economy. Hence Marx explicitly qualifies his version of the LTV by talking about the socially necessary labor time.
All labor is not the same, even restricting "labor" to time spent producing commodities of known price and use-value. Labor differs in intensity, desirability, training, education and marginal utility* (i.e. the time spent making the first widget creates more use-value than the time spent creating the last marginally useful widget). Again, Marx explicitly qualifies his version of the LTV by talking about the abstract labor time. If, for example, it were half as desirable to make hats as shoes (perhaps because of the obnoxious fumes), then the abstract labor time necessary to create a hat would be twice the actual labor time, and one hats would trade for one pair of shoes. Similarly, because it takes an additional seven to ten years (and a considerable amount of labor) to train a physician, the abstract labor time of an hour of a physician's actual labor is also magnified.
Also, the Marginal Utility Theory of Value (MUTV) does not contradict the LTV. The MUTV specifies which statistical properties of labor time constitute the price.
These quibbles notwithstanding, the LTV is, of course, not even close to being true, at least not by itself. For example, it's implausible to believe that in 2007 more than ten times more labor* was required to build a house in Sunnyvale, CA than in Youngstown, OH. It's implausible to believe that a Macintosh computer takes twice as much labor to build as a similarly configured Windows computer.
The best way, I think, to view the LTV is as a candidate "ideal" theory in the same sense as Newton's First Law of Motion. Neither bodies on Earth nor celestial bodies ever travel in straight lines at constant velocity. In a similar sense, the LTV can be recast with the proviso: In the absence of external economic forces, the price of a commodity is determined by the amount of socially necessary abstract labor time necessary to produce that commodity.
Of course, simply saying that the LTV is an "ideal" theory does not make it true, any more than calling Newton's First Law of Motion an ideal theory makes it true. There are specific scientific techniques that we can bring to bear on ideal theories to gain confidence in their truth.
It's important to understand that Newton never observed an object traveling in a straight line at constant velocity. The "net force" Newton was most interested in, of course, was gravity. Newton never actually observed one body exerting a net force on another body. The First Law of Motion (inertia) is explicitly contradicted by observation, and its primary modifier (which turns inertia into an complete* theory) was also not observable. (Worse yet, Newton had no clue how one body could actually exert a gravitational force on another.)
*At least regarding celestial bodies, which aren't affected by air resistance and aerodynamics, and leaving aside General Relativity for the time being.
We cannot justify inertia on "philosophical" grounds. The elegance and aesthetic appeal of the logical derivation from first principles is irrelevant. The "obvious" or intuitive appeal of those first principles is irrelevant. How can we empirically justify the FLM and the theory of gravity?
If we simply "induce" laws of motion from celestial bodies and bodies on the Earth, we end up with one law of motion for Mercury, one for Venus, one for the Sun, one for the Moon, etc., etc. and yet another for bodies on the surface of the Earth. (Curiously, we have (not counting aerodynamics) only one law of motion for all objects on the Earth's surface.) But if we hypothesize "unobservable" inertia and gravity, we end up with one law of motion which takes two independently observable* parameters: mass and distance. We cannot simplify all the motions of the celestial bodies without assuming inertia and gravity.
*More-or-less observable (and more directly observable than inertia and gravity). Density does not vary that much, and we can get a reasonable estimate of mass and distance from apparent size.
(It is a separate philosophical issue whether this sort of substantial simplification is at all epistemically relevant.)
If we consider LTV as an "ideal" partial theory, can we do the same sort of thing? There are a number of scientific tools available to us for testing the LTV.
The first tool is a general correlation. Correlation is not causation, but lack of correlation falsifies hypothetical causation. And there is indeed an apparent general correlation between actual labor time and price: jet airliners require more labor time per unit than houses, which require more labor time than cars, which require than computers, which require more than hamburgers, which require more than jellybeans, and the money prices show the same inequalities.
We can eliminate or control for "external" forces: Houses might vary in price between Sunnyvale and Youngstown without regard to labor time, but the difference in price of two houses in Sunnyvale or two houses in Youngstown will correlate more strongly to the difference in the amount of labor actually required to build the houses. A computer shipped by Amazon.com (i.e. a non-location-dependent commodity) to Sunnyvale will have almost exactly the same price as one shipped to Youngstown. (In a similar sense, inertia is more directly observable for bodies moving in nearly frictionless environments at right angles to the force of gravity.) The difference in price of two Windows computers will be more correlated to the difference in actual labor time, as will the difference in price of two Mac computers.
Better yet, we can independently observe "external" economic forces — geographical location, network effects, monopolies and monopsonies, etc. — and we can observe that two commodities with similar independently observable externalities will have similar "distortions" to the LTV.
Therefore we can conclude that the LTV + externalities has a similar empirical justification to inertia + gravity, and similar confidence is scientifically warranted in both.