Infections, wounds bleeding, broken devices, complications from brain implants like bleeding or brain damage. These are certainly bad outcomes, but I wouldn't say unexpected or something you wouldn't see with other animal tests for medical devices.
Keep in mind this description comes from Physicians Committee for Responsible Medicine which seeks to abolish animal testing entirely. Not an unbiased source.
If Musk's company were doing this alone, I might assume something bad is happening, but it's not, the tests are done in partnership with "California National Primate Research Center (CNPRC), a federally funded bioresearch facility at UC Davis".
I'd find it hard to believe a government run, non-profit center which are experts in primate research (and operating within a public university) aren't follow laws around animal testing and appropriate care and effort to prevent suffering.