The aim of our investigation was to examine the possible correlations between optical aberrations, angle kappa, angle alpha, and visual outcomes following cataract surgery. In total, 56 eyes of 28 patients were implanted with the Liberty 677MY trifocal intraocular lens (IOL). Pre- and postoperative higher-order aberrations, coma, astigmatism, angle alpha, and angle kappa were registered, along with uncorrected and corrected visual acuities at multiple distances. Visual acuity and contrast sensitivity defocus curves were plotted, and the areas under the curve were calculated 1 and 3 months postoperatively. Excellent visual outcomes were found at all distances. Patients reported low levels of dysphotopsia, and 96.4% of patients achieved complete spectacle independence. While angle kappa significantly decreased during cataract surgery (p = 0.0007), angle alpha remained unchanged (p = 0.5158). Angle alpha correlated with postoperative HOAs and had a negative impact on near vision (p = 0.0543). Preoperative corneal HOA and coma had a strong adverse effect on future intermediate and near vision. Residual astigmatism significantly affected postoperative intermediate vision (p = 0.0091). Our results suggest that angle kappa is not an optimal predictive factor for future visual outcomes, while angle alpha and the preoperative screening of optical aberrations might help patient selection prior to multifocal IOL implantation.