I am looking for a software/library or a web service/API that can detect problems in short samples of recordings of speech.
For example echo, clipping, pop, background noise...
Do you know of any tool that detects at least some of those?
Clipping and discontinuities can be detected by using the Izotope RX De-clicker and selecting "output clicks only". The resulting timeline will indicate where in the original material the discontinuities are. Not all of them will be full-on faults in the recording, you will have to use your ears to determine which of the candidate artifacts are actually real problems.