This study aimed to analyze the composition of fatty acids, with particular emphasis on the content of cis9trans11 C18:2 (CLA) acid, the content of minerals, and lipid quality indices in raw milk, pasteurized milk, and in yogurts produced with selected starter cultures enriched with Bifidobacterium bifidum. The GC-FID method was used to determine the fatty acid composition of those dairy products. To analyze the contents of microelements (copper, manganese, iron, and zinc) and macroelements (magnesium, calcium) flame atomic absorption spectrometry was used. The content of phosphorus was determined with the usage of the colorimetric method and the contents of sodium and potassium with emission method. Data analysis showed that such technologies as milk pasteurization and milk fermentation had a significant impact on the fatty acid profile and contents of micro- and macroelements. The lipid quality indices: atherogenicity index (AI), index thrombogenicity (TI), hypocholesterolemic/hypercholesterolemic index (H/H), and (n − 6)/(n − 3) ratio, were at similar levels in raw and pasteurized milk and yogurts produced. Starter culture type affected the content of cis-9,trans-11 CLA C18:2 acid in yogurts. Out of the starter cultures applied in the study, only the FD-DVS YC-X16 Yo-Flex starter culture with BB-12 caused a significant (p < 0.05) increase in CLA content. The CLA content of the yogurts produced using this starter culture was 2.67 mg/g fat. In raw milk, pasteurized milk, and the second batch of yogurts, the content of cis-9,trans-11 C18:2 acid was significantly lower and reached 2.26 mg/g fat, 2.17 mg/g fat, and 2.30 mg/g fat, respectively. The study indicated that, when it comes to being a source of minerals, yogurts were better than milk. Yogurts were also characterized by significantly (p < 0.05) higher contents of all micro- and macroelements taken into account in this study than the raw milk used to produce them.