I just read Cormac Mccarthy's "All the Pretty Horses," and the English speaking American characters frequently interact with Spanish-speaking characters in Spanish, despite their lack of education. In other films and movies, I have seen characters that can speak anything from Spanish to English to Navajo. In particular, it is assumed that they speak this language.
Would it be typical for a 1940s resident of El Paso to speak both Spanish and English? Would a resident of Flagstaff, Arizona know Navajo?
Flagstaff and El Paso are very different places. El Paso has been a heavily Hispanic town as long as it has existed and some degree of multilingualism would have been reasonably common, if not universal. The 1940s in particular were a decade of huge immigration for the city as laborers moved in to fill American jobs left vacant by the war and increasing industrialization.
Flagstaff on the other hand is very much an Anglo town. Although it was nominally the political center of Northern Arizona, those politics excluded native participation. The tribal reserves are deliberately far from Flagstaff on the dry mesas of the Colorado Plateau. The city's population at the first census in 1960 recorded only 4% of inhabitants as being of native descent. However, it's worth noting that to the East / Southeast of Flagstaff is a mountainous area known as the Mogollon Rim. The towns and villages in this area (including Holbrook, which isn't strictly in Rim country) are heavily Mormon. Mormons have a tradition of doing missionary work abroad and many of the people from this area spent that time in Mexico during the early 20th century. Familiarity (if not full fluency) with Spanish was very common among rural Mormon communities as a result.
A resident of Flagstaff would not have known Navajo. I'll quote part of an old answer regarding the Navajo Code Talkers:
It's an extremely complicated language that makes use of a number sounds that simply don't exist in English, making it very difficult to learn if one isn't raised with it. Chester Nez, one of the original 29 Code Talkers, said "emphasis on the wrong syllable, a slight change in tone, or a glottal stop could totally change a word's meaning [...] Several white Marines who'd grown up on the Navajo Reservation and knew quite a bit of Navajo later applied to code talker school. But there were always words or syllables they could not pronounce correctly, so they didn't make it as code talkers." In 1942 only about 30 non-Navajos spoke it, and most of them were traders, missionaries, or their children (and as Nez demonstrates, they didn't speak it fluently).