How to evaluate the quality of speech-to-text data without access to the true labels?
There is at least one way:

Create/Acquire a grammar model for the language spoken (there are several such models for various languages used in NLP)
Test the transcripts for beign grammaticaly/syntacticaly correct.
This assesment will at least rule out gibberish and most of transcripts that do not correspond to valid sentences of the language spoken