Well...there's "backwards sneezing". Scares the hell out of most new toy breed owners the first time it happens, but it's common in the small breeds and not really a problem, as such.
Otherwise, one of the most common health issues with Chihuahuas is bad teeth - many Chis need dental work by the time they're two years old. As such, it's highly recommended to brush their teeth, at least a few times a week to help. The breed itself doesn't have much in the way of genetic health concerns or issues.
They're usually pretty quirky, and having such a tiny dog is an adjustment for sure. I grew up with big dogs - 120lbs shepherd/Malamute crosses who were brothers, and the best dogs. I'm a big dog person, but Chihuahuas are my weakness and I've had them in my house for 14 years. Things like, Chihuahua proofing any fencing in the back yard - they fit through the TINIEST spaces under the fence or between posts! Or, always being supervised when in my yard - a large raven could easily go after my smallest boy, never mind hawks, owls, or eagles. Just things like that