Five palladium(II) complexes of substituted salicylaldehydes (X-saloH, X = 4-Et2N (for 1), 3,5-diBr (for 2), 3,5-diCl (for 3), 5-F (for 4) or 4-OMe (for 5)) bearing the general formula [Pd(X-salo)2] were synthesized and structurally characterized. The crystal structure of complex [Pd(4-Et2N-salo)2] was determined by single-crystal X-ray crystallography. The complexes can scavenge 1,1-diphenyl-picrylhydrazyl and 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) radicals and reduce H2O2. They are active against two Gram-positive (Staphylococcus aureus and Bacillus subtilis) and two Gram-negative (Escherichia coli and Xanthomonas campestris) bacterial strains. The complexes interact strongly with calf-thymus DNA via intercalation, as deduced by diverse techniques and via the determination of their binding constants. Complexes interact reversibly with bovine and human serum albumin. Complementary insights into their possible mechanisms of bioactivity at the molecular level were provided by molecular docking calculations, exploring in silico their ability to bind to calf-thymus DNA, Escherichia coli and Staphylococcus aureus DNA-gyrase, 5-lipoxygenase, and membrane transport lipid protein 5-lipoxygenase-activating protein, contributing to the understanding of the role complexes 1–5 can play both as antioxidant and antibacterial agents. Furthermore, in silico predictive tools have been employed to study the chemical reactivity, molecular properties and drug-likeness of the complexes, and also the drug-induced changes of gene expression profile (as protein- and mRNA-based prediction results), the sites of metabolism, the substrate/metabolite specificity, the cytotoxicity for cancer and non-cancer cell lines, the acute rat toxicity, the rodent organ-specific carcinogenicity, the anti-target interaction profiles, the environmental ecotoxicity, and finally the activity spectra profile of the compounds.