Falls among elderly patients with musculoskeletal disorders represent a leading cause of injury-related hospitalization, disability, and mortality worldwide, with approximately 30% of community-dwelling adults aged 65 and older experiencing at least one fall annually. Current fall risk assessment methods including questionnaires, clinical rating scales, and instrumented walkway tests are limited by subjectivity, low sensitivity, and requirement for specialized equipment or personnel. This paper presents FallNet, a novel deep learning-based vision system for automated, non-contact gait analysis and fall risk prediction in elderly patients with musculoskeletal disorders. The framework processes monocular video from standard RGB cameras (smartphone or webcam) to extract 3D skeletal keypoints using a lightweight pose estimation backbone (MediaPipe or BlazePose), then computes a comprehensive set of 24 spatiotemporal and kinematic gait parameters including stride length, step time variability, gait speed, double support time, arm swing asymmetry, and joint angle trajectories. These features feed into a multi-scale temporal convolutional network (MS-TCN) with attention mechanism that classifies fall risk into three categories (low, moderate, high) and predicts prospective falls over a 12-month horizon. We validate FallNet on a prospective cohort of 342 elderly patients (mean age 74.6 ± 7.8 years, 62% female) with diagnosed musculoskeletal disorders (osteoarthritis, osteoporosis, sarcopenia, lumbar spinal stenosis) recruited from two geriatric outpatient clinics. Patients performed a standardized 10-meter walk test while being recorded by a single RGB camera, with concurrent 3D motion capture (gold standard) and 12-month prospective fall diary. FallNet achieves 89.4% accuracy in three-class fall risk classification (sensitivity 91.2%, specificity 88.1%, AUC-ROC 0.94) and predicts prospective falls with F1-score of 0.87, substantially outperforming clinical scales (Timed Up and Go: 68.3% accuracy; Berg Balance Scale: 71.2% accuracy; p<0.001 for all comparisons). Key gait parameters predicting fall risk include: gait speed <0.8 m/s (odds ratio 4.2), stride time variability >5% (OR 3.8), double support percentage >25% (OR 3.5), and arm swing asymmetry >30% (OR 3.1). The system runs in real-time (25 FPS on smartphone CPU) and requires no specialized equipment, making it suitable for deployment in primary care clinics, rehabilitation centers, and home settings. Explainable AI techniques (Grad-CAM and SHAP) identify which gait phases and body segments contribute most to fall risk decisions, enhancing clinical interpretability. This work establishes that vision-based deep learning gait analysis can provide accurate, accessible, and objective fall risk screening in elderly patients with musculoskeletal disorders, enabling early intervention and fall prevention strategies.