What are good ways to detect signal clipping in a recording?
I was in the middle of typing an answer pretty much exactly like Yoda's.  He's is probably the most reliable but, I'll proposed a different solution so you have some options.



If you take a histogram of your signal, you will more than likely a bell or triangle like shape depending on the signal type. Clean signals will tend to follow this pattern. Many recording studios add a "loudness" effect that causes a little bump near the top, but it is still somewhat smooth looking. Here is an example from a real song from a major musician:



Here is the histogram of signal that Yoda gives in his answer:



And now the case of their being clipping:



This method can be fooled at times, but it is at least something to throw in your tool bag for situations that the FFT method doesn't seem to be working for you or is too many computations for your environment.