One crime-oriented warning if you're out prowling the boonies: on occasion when you're out in theoretically empty country, you will see a small plane drop below the local horizon and then climb back out. Do not investigate. The odds are quite good that this plane is departing minus a load of controlled substances that was delivered to someone waiting below who won't be glad to see you. Scary encounters have occurred under such conditions not only with the recipients of this contraband, but also with DEA agents waiting to apprehend them.
The usual safety concerns about rural areas apply here, with a little extra emphasis on getting help. The remote parts of northwest New Mexico are really out in the boonies, and help can be a very long time in arriving, particularly if you're hiking or river running. This problem is exacerbated by the fact that cellular phone coverage is spotty owing to distances and terrain. You may find it difficult to arrange rescue via cell phone if something does happen to you on a river or a trail. When venturing into the backcountry, it's thus a good idea to carry a little more in the line of emergency gear and supplies than might otherwise be your usual practice. Extra water is also important, as water sources are few and commonly contaminated.
It seems incongruous to raise safety issues involving flash floods in an area as dry as this one, but flash floods do claim lives here. The limited rainfall tends to come in brief but extremely violent thunderstorms that can drop a lot of water in a short time, onto a landscape that the water generally doesn't soak into, owing to desert varnish, caliche, etc. Use caution when entering gullies and washes, even if there don't seem to be any storms nearby; flash floods can occur far downstream of the storms that create them.
talk
If you happen to speak Navajo, yah-te-hey, and you'll likely have a chance to practice it here. English is the more universal language of the region, however. A smaller fraction of the population speaks Spanish than in most other parts of New Mexico, and speakers of other languages except Zuni are rare.