I touched briefly yesterday on avoiding websites that make random assertions without backing them up. I should reiterate and clarify that this applies also to books and articles, and even to chapters within otherwise solid books.
Beware the Trendy
When a topic becomes popular, look out. It's often romanticized up one side and down the other. Holes in the record are filled in to "look nice" and appeal to a reading public that likes a neat picture rather than an accurate one. I'd currently look twice at any book on pirates or Celtic traditions.
Spirituality Is Separate
Whatever someone's faith has lead them to believe is spiritually, metaphysically or literally true is their own business, in my opinion. However, evidence that appeals to the spirit is often not the evidence that we would like to use to support historical (or other) research. To everything there is a season. Do not wear your parka to the beach. Be very, very careful about using religious texts (anything from the Bible to "Celtic Magic") in your research.
Remember Why They Call It Oral Tradition
I am deeply, deeply suspicious of any book which claims to have unearthed an ancient oral tradition, handed down unchanged from ages ago, as a historical source. The "ancient oral tradition" is actually datable only to the time it was collected. It may be older but it would be darn hard to say for sure.
Singers are especially susceptible to claiming "oral tradition" to document ballads. This does not really fly, especially when there may be internal evidence in the ballad (language use, musical structure, even themes) which could be used to actually attempt to date it.
Watch for Sudden Leaps from the Specific to the General
In college, I read what was probably someone's dissertation: a very focused account of a particular English manor, as seen through its court records. Keen. Then in the last chapter, after having spent the preceeding three demonstrating how idiosyncratic people and customs could be, the author began making very large generalizations about "women in England." While her last chapter wasn't awful, it wasn't nearly as well-supported as the rest of the book. It read more like a generalized encyclopedia entry.
More pathologically, you sometimes find authors substituting anecdotal evidence for statistical evidence. "This happened once in this particular place; ergo, since so many records have been lost, this must have actually been a widespread custom of which this is the only surviving record." It ain't so, Joe.
"Everyone Knows" and "Traditional"
Similarly, appeals to "everyone knows" should be translated as, "I couldn't be bothered to find citations." "Everyone" is frequently wrong, or at least has an overly simplified view of things.
Similarly, music, dances, or folk crafts which are said to be "traditional" are often actually "not researched." I've seen an assortment of copywritten 20th century songs presented innocently as "traditional." Heck, I've seen them recorded and cited on CD jackets that way.
Watch Out for Agendas and Assumptions
As an example, there are real-life political ramifications to a "Celtic" identity. It's the basis for independence movements in Wales, Scotland, and elsewhere - so certain authors have a vested interest in portraying a certain kind of "Celticity" which may or may not have anything to do with how the Celtic tribes saw themselves. A search for "Anglo-Saxon" on Yahoo! Groups turns up some history buffs as well as some white power groups. The Victorians were notorious for bowdlerizing or romanticizing certain parts of history.
More mundanely, an author may have a thesis to prove. Not a small number of history books are cleaned and published dissertations, and a classic fault of the PhD is to try and make the case for one's thesis stronger than it actually is. All possible positive arguments, from the sound to the shakey, are marshaled in defense of the thesis. Strong, plausible negative arguments are beaten to a pulp by any means possible, rather than accepted as possible alternative interpretations. (And as a new researcher, you should yourself watch out for this tendency in your own documentation...)
There's also what the evidence is versus what we perceive it to be. Until fairly recently, for example, Iron Age graves in Europe were sexed by their grave goods. Spears and weapons meant men; spindles and jewelry meant women. Now, advances in DNA analysis have revealed that some of the warriors were women as well! Try to distinguish what something is (a skeleton with a spear) from what we think it means. Of course at some point, you want to draw some kind of conclusion, but being very clear about what you know versus what you assume will make revisiting that conclusion with new evidence easier later on.