A simple, time efficient, analytical model incorporating heterogeneities and body dimensions around a point ¹⁹²Ir source is generalized for accurate dosimetry around commercially available ¹⁹²Ir brachytherapy sources. The generalized model was verified in dosimetry of a clinical ¹⁹²Ir high dose rate prostate monotherapy application, involving 16 catheters and 83 source dwell positions, through comparison with corresponding treatment planning system data. The computational time efficiency and accuracy of the proposed model allowed the assessment of the impact that uncertainties in source dwell positions and catheter reconstruction may have on dose distributions, and how these could potentially affect the clinical outcome. Results revealed that a 0.1 cm catheter reconstruction uncertainty and a 0.15 cm source position uncertainty along the catheter lead to a dose uncertainty of less than 2% for doses lower than 200% of the prescribed dose, reaching up to 5% for points lying in close proximity to the catheters. These uncertainties were found to have no impact (less than 1%) on dose volume histogram results of both the planning target volume and the urethra. A catheter reconstruction uncertainty as high as 0.2 cm results in a dose uncertainty greater than 2%, reaching up to 9%, only for points inside the 150% contour. However, even in this case, the impact on dose volume histogram calculations is less than 3%.