(1) Background: Patient safety is a discipline of health care management aiming to prevent and reduce errors and harm to patients. The assessment of knowledge and attitudes on patient safety among students in physical therapy is still scarce; no studies have yet explored the changes that internship periods may produce. Objectives: 1. to determine the attitudes and knowledge of students in physical therapy with respect to patient safety in a Spanish University; and 2. to explore changes following a practical internship period. (2) Methods: Longitudinal study. Data from the Attitudes to Patient Safety Questionnaire III (APSQ-III) before and after the internship period were obtained from an initial sample of 125 students and average positive response rates were compared. (3) Results: “Team functioning”, “Importance of patient safety in the curriculum”, and “Error inevitability” displayed the highest scores, in accordance with the current literature. After the internship period, the dimensions “Patient safety training received” (p = 0.001), “Error reporting confidence” (p = 0.044), and “Professional incompetence as an error cause” (p = 0.027) showed significant changes. (4) Conclusions: The current study, highlighting areas of strengths and weaknesses in the knowledge and attitudes of students in physical therapy towards patient safety, may be a foundation to adopt tailored programs to enhance students’ competencies in patient safety.