Free apps will usually come with adverts built in. A pain in the arse, but if the app itself is good enough you can usually live with them. Often there's an option to purchase an ad-free version and if you really like it, it's worth doing that. It might only cost two, or three, quid.
I use the seismograph app and Radio Paradise (although more often through VTuner). Vibration is useful as well. I have a stand-alone sound pressure meter from work anyway, but I'll give the spectrum analyser app a go as it will be much less cumbersome than the one we have at work.
Of course I also use the Naim app for the NDX etc and the Fidata app for the server although it is a bit flaky!
Be wary of apps that ‘measure’ dB levels on your phone. I used one a while back and compared it to a professional, calibrated microphone and it was only about 20db off lol.
Also who knows how linear the mic is as well...
I have no experience of other things like vibration detection but I presume the same warning applies to everything; especially when your talking the Android market, where there’s huge scope for variation between models, which I doubt the software has been written to compensate for.