(1) Background: Geriatric patients are at high risk of complications of Coronavirus disease-2019 (COVID-19) and are good candidates for antiviral drugs. (2) Methods: A retrospective study of electronic health records (EHRs) aiming to describe antiviral (nirmatrelvir and ritonavir (nirmatrelvir/r) or remdesivir) use, drug–drug interactions (DDIs) and adverse drug reactions (ADRs) in elderly patients (75 and over), hospitalized with mild-to-moderate COVID-19 between July 2022 and June 2023. (3) Results: Out of 491 patients (mean age: 86.9 years), 180 (36.7%) received nirmatrelvir/r, 78 (15.9%) received remdesivir, and 233 (47.4%) received no antiviral therapy. No association was found between the choice of antiviral and the demographic or medical data. No serious ADR was observed. Nirmatrelvir/r dosage adjustment was inadequate in 65% of patients with renal impairment. In total, 128 patients (71%) on nirmatrelvir/r had potential pharmacokinetic DDIs, with 43 resulting in a possibly related ADR. In the remdesivir group, pharmacodynamic DDIs were more frequent, with QTc prolongation risk in 56 patients (72%). Only 20 patients underwent follow-up ECG, revealing QTc prolongation in 4. (4) Conclusions: There is an underutilization of antivirals despite their justified indications. Nirmatrelvir/r dosage was rarely adjusted to renal function. Dose adjustments and closer monitoring are needed due to the high risk of drug interactions.