The biggest clue as to how valuable a books is likely to be is the publisher. If the book is published by a university press or an scholarly publisher (eg: Boydell, Brill, etc), then there's a good chance it will have a fairly high standard of content. This can be further enhanced by looking for academic reviews of the book and reading them to find out what the faults and weaknesses of the book are (and every book has some). Often the reviewers will mention works that deal with the weaknesses in the text they are reviewing, or which they think have a better approach or conclusion. These can then be added to your reading list for a more complete picture.

It's also important to critically evaluate every book you read yourself. If something doesn't feel right, check the source given and then look for others that might offer a different opinion. The Amazons: Lives and Legends of Warrior Women across the Ancient World, for instance, contains part of Xenophon's Anabasis taken out of context (re: dancing girl performing a male war dance) in order to show that the women with the Greek army had some fighting skill, rather than the whole thing just being a combined mockery of the Persians/intimidation of Persian allies. There's also a source cited on a distinctive ring pattern in nomadic wedding dresses that Adrienne Mayor attributes to a past practice of women wearing mail, but which her source denies in the most unambiguous of terms.

Other times you'll find two sides to a debate that is, or was at the time of writing, still ongoing, such as the Gillingham orthodoxy about medieval battle avoidance and the Rogers heresy about medieval battle seeking. In these cases you need to evaluate both positions yourself and look for any more recent work to see whether one side or the other has become the new orthodoxy (although if you disagree that's still fine!).

With popular history books, a big indication as to the quality of the scholarship are the qualifications of the author. If they have a degree in the subject they're discussing, and have published any academic works in that field, then they're likely to have good material in their book, especially if there is a large bibliography and/or reference section. Jim Bradbury and his The Medieval Siege is a great example of this, and his book is still one of the best "textbooks" on the subject, although it has been superseded by more academic books. Again, looking to see if any academic reviews of the books is handy, as the better pop history books will end up being reviewed by academics.

In addition to the advice already given, I would like to point out a couple others.

Firstly, check the About the Author page. There always is one, especially with nonfiction. A lot of the time, "popular history" is written by journalists, and while their work is not necessarily bad or wrong, it's better to find someone who has a professorship listed in their accomplishments.

Additionally, if you find a book that you like and that you feel is accurate, check their references! The Works Cited page will lead you to a treasure trove of books and articles written on the subject that the author him/herself believed were credible enough to cite.

Nothing is inherently foolproof, of course, as many professors will write books that are uninformed or operating on incomplete histories, but those are good starting points.

I teach research writing to college students and we go over how to properly vet sources, so I can throw in a few tips to expand on the other good advice here.

A big thing to look out for is author bias. Although a little bias in all writing is inevitable, in a historical context a good academic will go out of his/her way to approach a topic in a neutral manner and offer copious sourcing for any opinion put forward (as mentioned above). Be wary of sweeping conclusions made without evidence shown to back them up, as well as emotionally loaded language. If it looks like the author is writing from a place of anger or indignation, that raises a lot of red flags for me. Writing with emotion instead of reason often clouds even the best arguments. I've unfortunately dealt with this plenty, as my preferred area of research is so fraught with bias that the authors I value the most will address it at the outset as a problem in the field.

In general, if a good writer wants to make a persuasive argument, s/he will give the most well-rounded explanation of the topic possible, to illustrate all the sides before explaining why s/he believes the chosen one. Be wary if any one side of a situation or issue is being downplayed or ignored. That tends to signal the author is on shaky logical ground and does not want to expose weaknesses in the thesis.

Sometimes with this sort of thing the only solution is trial and error; if you read several titles in the same area, you might come across information that seems accepted among a wide variety of scholars. That can often be considered sound information. Other times, you may experience conflicting viewpoints about the same topic and that will signal that there may not be one accepted version given the currently available research.

Finally, considering the age of the source also helps. If there's been a recent major discovery on a topic, it can often render older titles on it outdated or obsolete. This comes up more often in fields like science and technology, but it can happen with history, too. Still, older viewpoints can lend context for a particular time period. I tracked down a book written in the 1960s about Russia's viewpoint of its non-native ethnicities, for instance, because I was interested in a Soviet-era perspective on that. I would not consider it current for 2017 on the same topic, as the region has changed drastically since then.

Hope this helps!