The paper presents the results of a laboratory experiment of mesophilic single-stage anaerobic digestion performed to verify the possibility of early detection of process instability and reactor overload by evaluating the course of dissolved hydrogen concentration of the main intermediate. The digestion process was run in a Terrafors IS rotary drum bioreactor for 230 days. The substrate dosed on weekdays was food leftovers from the university canteen. At an average temperature of 37 °C, an organic loading of volatiles of 0.858 kg m−3 day−1 and a theoretical retention time of 259 days, biogas production of 0.617 Nm3 kg VS−1 was achieved with a CH4 content of 51.7 vol. %. The values of the established FOS/TAC stability indicator ranged from 0.26 to 11.4. The highest value was reached when the reactor was overloaded. The dissolved hydrogen concentration measured by the amperometric microsensor ranged from 0.039−0.425 mg dm−3. Data were statistically processed using Pearson’s correlation coefficient. The correlation of the hydrogen concentration with other parameters such as the concentration of organic acids was evaluated. The value of Pearson’s correlation coefficient was 0.331 and corresponded to a p-value of 0. The results confirmed a very low limit of the hydrogen concentration at which the microbial culture, especially methanogens, was already overloaded. The amperometric microsensor proved to be rather unsuitable for operational applications due to insufficient sensitivity and short service life. The newly designed ratio of dissolved hydrogen concentration to neutralizing capacity was tested but did not work significantly better than the established FOS/TAC stability indicator.