Well, you could use your smartphone's accelerometer to verify the equations for centrifugal force, or its GPS to verify parts of special and general relativity, or the fact that its chip functions to verify parts of quantum mechanics.

These don't feel like the are quite comparable to each other. I do really trust the accelerometer to measure acceleration. If I take my phone on the merry-go-round and it says "1.2 G", I believe it. I trust my GPS to measure position. But I only take on faith that the GPS had to account for time dilation to work right -- I don't really know anything about the internals of the GPS and so "trust us it works via relativity" isn't really compelling at an emotional level. For somebody who worked with GPS and really knew about the internals of the receiver, this might be a more compelling example.

But I'm not sure how you can legitimately claim to be verifying anything; if you don't trust those laws how can you trust the phone? It would be like using a laser rangefinder to verify the speed of light. For this sort of thing the fact that your equipment functions is better evidence that the people who made it know the laws of physics, than any test you could do with it.

Yes of course. In real life I'm perfectly happy to take on faith that everything in my undergraduate physics textbooks was true. But I want to experience it, not just read about it. And I think "my laser rangefinder works correctly" doesn't feel like experiencing the speed of light. In contrast, building my own rangefinder with a laser and a timing circuit would count as experiencing the speed of light.

I am starting to worry that my criteria for "experience" are idiosyncratic and that different people would find very different science demonstrations compelling.