Qualifications
Generally, every single health and safety specialist will have a bachelor's degree. All the cool kids are doing it, and by "cool" we mean "employable." After all, would you trust your health and safety or that of your family members to somebody who doesn't have a really nice piece of paper saying they know a bunch of stuff?
The field of study for your bachelor's can vary, but it should have to do with where you see yourself inspecting. You industrious people who want to work around construction, shipping, or insanely cool cars, should focus on engineering. If you're more of a neat freak, aiming to protect the community from the ravages of undercooked chicken, majoring in biology or public health will be helpful.
Physics, mathematics, chemistry, anatomy, statistics, and even nutrition or nursing have their uses for an inspector (source), so you'll need to figure out which one gets you as close to your dream inspection (dreamspection?) job as possible.
Some fields or employers will also require certification. Most cities and states have their own certification programs for restaurant inspectors, while all nuclear plant inspectors need a Federal certification to work.
That's right: technically speaking, Homer Simpson is a Federally-approved employee. If he can pass the test, surely you shouldn't have an issue.