I was going to do a test myself, comparing my Android phone and tablet to the Radio Shack meter. I went to the Play store and was going to download the free version of the highest-rated one. Right there in the vendor's description was a lengthy caveat about the limitations of such devices.
He noted that the circuitry is optimized for speech frequencies and conversational levels, so don't expect any low-frequency response below 300Hz. You can see the obvious problem already: frequencies below 300 Hz represent 99% of the sound energy. Note that in the tests dmbaer linked to above, the test frequencies are 1 KHz and 8 KHz.
He also gives maximum SPLs for some different devices, ranging from as low as 80 dB (Samsung Galaxy S3, which happens to be my phone) to 100 dB (for the Moto Droid). My tablet maxes out at 91 dB. Makes sense; there is going to be a built-in limiter in there. That means the accuracy likely falls off the louder you get.
I think these apps would suffice for their intended purpose, which is not studio calibration duties but rather environmental testing. If you think you've got grounds for an OSHA complaint at your workplace, one of these apps would probably give you ammunition. Just don't expect OSHA to show up with an iPhone.