What happens to the structure of tetracyclines when they expire?
Apparently the culprits are anhydro-tetracycline (ATC) and 4-epianhydrotetracycline (EATC) - see Determination of tetracycline and its major degradation products by liquid chromatography with fluorescence detection. J. Pharm. and Biomed. Anal. 18 (1998), 839-845 for structural information and references to toxicity of those byproducts as known at the time of publication.

It is worth noting that renal tubular acidosis (RTA) - the condition that was reported in 1963 to have been precipitated by ingestion of expired tetracycline - is not presently considered as much of an issue as it was at the time (see this review). Finally, this piece in the New York Times from 2014 (entitled Do some drugs become dangerous after expiration?) has more information and references concerning tetracycline and RTA.