Background: Older persons are more likely to have multiple chronic diseases, leading to the simultaneous use of many medications. This situation results in increased drug-related problems (DRPs), which are the causes of adverse health outcomes. Therefore, we aimed to evaluate the prevalence of and associated risk factors for exposure to >1 criterion of DRPs among older adults admitted to a tertiary care hospital. Methods: We conducted a cross-sectional study involving 357 participants aged ≥60 years admitted to Ramathibodi Hospital from 1 February 2022 to 30 November 2022. The participants were evaluated for baseline characteristics, medications and DRPs and were classified into two groups, according to their exposure to DRPs: patients with exposure to ≤1 criteria and patients with exposure to >1 criterion of DRPs. Multivariate logistic regression analysis was performed to determine the independent risk factors for exposure to >1 criterion of DRPs. Results: Overall, 205 (57.4%) patients experienced >1 criterion of DRPs. Approximately 67.8%, 71.7% and 7.6% of the participants were exposed to at least one potentially inappropriate medication (PIM), drug–drug interaction (DDI) and adverse drug events (ADE), respectively. The most frequently prescribed PIMs were proton pump inhibitors (PPIs) (17.3%). Antineoplastics (48.1%) were the most frequently drug class related to ADEs. Overall, 37% of the ADEs in the current study were considered preventable ADEs. After adjustment for potential confounders, polypharmacy and the use of proton pump inhibitors, hypoglycemics, diuretics, psycholeptics, psychoanaleptics and cardiac therapy medications were correlated with a higher risk of exposure to > 1 criterion of PIMs, DDIs or ADEs. Conclusions: Therefore, comprehensive medication reviews and careful medication prescriptions are recommended in the geriatric population.