At her terrific Appellate Daily blog, Michelle Olsen has this post about the four federal circuit courts of appeal that do not yet post audio files of oral arguments on their websites. The Tenth Circuit is one of them. To obtain a copy of the audio of an oral argument, the Tenth Circuit requires that one file a motion, albeit such motions are routinely granted. (By the way, I highly recommend following Ms. Olsen on Twitter, @AppellateDaily, because she tweets frequent updates about the federal appellate courts).
Unfortunately, New Mexico’s state appellate courts also do not post audio recordings of oral arguments online, though one can obtain a CD of oral argument audio by paying a small fee (e.g. in March I obtained a CD of an oral argument recording from the New Mexico Supreme Court for $1). I do not know what technical challenges would face the state courts in making the audio recordings available online, but let’s hope those can be overcome soon.