How useful are early 20th C books on art materials?

This is a pretty broad question. Where manufactured art materials are concerned, the most current information about ingredients, long-term performance and safety are obviously better than old data, so out-of-print books are progressively less useful in this regard. As research materials for learning the craft of painting, however, older handbooks can be really valuable. Craftsmanship is about learning standards of performance, how to define them for oneself and how to meet those standards. In my opinion, a book like The Technique of Painting by Moreau-Vauthier, for instance, still has a lot to offer the skilled trade of painting, even if many of the materials covered are now obsolete. 

Matthew is correct about the writing about craft, modern ingredients, long-term performance, and safety. As to painting practice, the answer is very complicated. The Carlyle book is rather unique, but its purpose it to document the manuals of the 19th century British writers on the subject and the materials produced at that time. It is accurate about that, but it documents a period in time when writers were the most misguided about painting practice. I would not use the included recipes as models of good painting practice.   In many ways, these are the types of books that remain relevant for the longest period of time as they do not rely on the interpretation of incomplete data.
As to more recent writers on the craft of oil painting, there is a famous book of painting formulas that contains many, many recipes that should NEVER be added to oil paint. Maroger was just completely wrong about just about everything he included in his infamous book. Mayer was very good in spirit, although today his recipes for glazing mediums containing 50-50 oil-damar are considered very problematic. Some of his tenants are timeless while other suggestions in his tome are obsolete today. I can think of no inaccuracies in Gottsegen, and his book is very useful if a bit conservative. The situation today is far more simple about pigments, as long as you have the actual pigment number it should be easy to find information about permanence. Painting practice is more complicated. If it were not, there would be little use for a forum like this one.
Some older books are generally on the mark even though they have some of the particulars wrong. Most of the descriptions that attempt to outline the methods and materials of the Old Masters, however, were completely off base. Doerner was so off that much of what he suggested created paintings that are already in very bad condition. A. P. Laurie and Church are less problematic and some of the 19th century volumes are better since they focus on interpreting old manuscripts, although, even in this, we need to be very careful. Few of these are authoritative. Even Thompson’s Cennini translation has been shown to contain over 400 mistakes, some of these are quite crucial. There are new and authoritative translations of both Cennini and the Strasbourg Manuscript. The translations of De Mayern included in Fels’s book is also problematic as it is an English translation of a less than perfect German translation of the original manuscript.
We do live in a golden age of publications on historical painting practice. Most current monographs on Old Master painters contain a technical section that can provide real information. However, to be absolutely honest, even the early issues of the National Gallery Technical Bulletin should not be read as gospel about historical painting practice as they based some of their assumptions on analytical instrumentation and data that is now known to be insufficient to make definitive conclusions. The most obvious example is their initial pronouncements that tempera grassa was a very common medium in 15th C. Italy based on their early chemical analysis. We know know this analysis is more complicated than they initially thought and most authorities on the evolution of painting in Italy no longer accept that supposition. For the most part, though, TNGTB is a wealth of concrete information about documented historical painting practice. Publications by conservation scientists and conservators working together, published in the last decade or two can generally be relied on….as far as we know today.
This is probably a less than satisfactory response but it is an accurate description of the situation as it is.

I suppose it depends on what one expects to extract from the resource, and how to apply the information. If you really think you’re going to find the verified secrets of the Old Masters, those old books are going to break your heart. It has to be acknowledged that Moreau-Vauthier’s reverse-engineering of Roman encaustics is just not useful to a painter today. Then again, he happened to study under Jean-Léon Gérôme, and he wrote books on how to paint- that’s worth a look. Read The Painter In Oil by Daniel Burleigh Parkhurst and see if it doesn’t make you want to step up your game. The best of the old books have at least one valuable lesson to teach: there are some things a painter must be able to do very well, each time, according to a professional standard. That lesson was attractive to many in my generation, who were taught by old AbEx adherents at a time when traditional skill was too often derided.