Buffelgrass has become well known as an invasive exotic species, but many other dangerous exotics threaten parts of the southwest and have garnered much less attention. One in particular comes to mind from my experiences: Sahara mustard (Brassica tournefortii). This mustard has an affinity for sandy or bottomland soil in the middle and especially lower elevation Sonoran Desert. It has spread rapidly across large areas of southwestern Arizona and southeastern California. I've recently seen it in several disturbing places including the Pinacate Biosphere Reserve, in Bear Canyon in the Catalinas, and Saguaro National Park (east and west). The Arizona/Sonora Desert Museum has a good webpage on this mustard.
Another species we should be keeping a close eye on is the Eurasian collared dove, which appears to be exploding in abundance in Arizona and Sonora since the 2000s. It may start displacing native doves such as the White-winged and mourning dove, among others. Every year I see more of this species in more different places around the southwest US and Sonora. They seem to prefer human settlements, but are not exclusive to them.