The study demonstrated the effects of precursor feeding on the production of glucosinolates (GSLs), flavonoids, polyphenols, saccharides, and photosynthetic pigments in Nasturtium officinale microshoot cultures grown in Plantform bioreactors. It also evaluated the antioxidant and antimicrobial activities of extracts. L-phenylalanine (Phe) and L-tryptophan (Trp) as precursors were tested at 0.05, 0.1, 0.5, 1.0, and 3.0 mM. They were added at the beginning (day 0) or on day 10 of the culture. Microshoots were harvested after 20 days. Microshoots treated with 3.0 mM Phe (day 0) had the highest total GSL content (269.20 mg/100 g DW). The qualitative and quantitative profiles of the GSLs (UHPLC-DAD-MS/MS) were influenced by precursor feeding. Phe at 3.0 mM stimulated the best production of 4-methoxyglucobrassicin (149.99 mg/100 g DW) and gluconasturtiin (36.17 mg/100 g DW). Total flavonoids increased to a maximum of 1364.38 mg/100 g DW with 3.0 mM Phe (day 0), and polyphenols to a maximum of 1062.76 mg/100 g DW with 3.0 mM Trp (day 0). The precursors also increased the amounts of p-coumaric and ferulic acids, and rutoside, and generally increased the production of active photosynthetic pigments. Antioxidant potential increased the most with 0.1 mM Phe (day 0) (CUPRAC, FRAP), and with 0.5 mM Trp (day 10) (DPPH). The extracts of microshoots treated with 3.0 mM Phe (day 0) showed the most promising bacteriostatic activity against microaerobic Gram-positive acne strains (MIC 250–500 µg/mL, 20–21 mm inhibition zones). No extract was cytotoxic to normal human fibroblasts over the tested concentration range (up to 250 μg/mL).