Simple -- a national registry that could be easily accessed by service providers that need the information. The technology is relatively simple, but the government is totally incompetent, so it will never happen. Another solution, though not perfect, is a government-issued ID w/ some anti-counterfeiting technology.
And before people jump on my back, I'm not saying the nature of a person's disability needs to be disclosed; just a simple way to provide a verified method to see if a person is or is not eligible for disability status. This would also keep all of those "comfort pet" owners from claiming service dog status.
Kurt