If you see mold on your kimchi, it's generally best to discard it for safety reasons. While some molds are harmless, it's difficult to determine the type of mold present without testing, and some can produce harmful mycotoxins.
Kimchi is a fermented food, and fermentation involves the growth of beneficial bacteria. However, unwanted molds can also grow, especially if the kimchi isn't stored properly or if the fermentation process wasn't ideal. The fuzzy mold spots you're seeing indicate that undesirable microorganisms have taken hold.
While you might be tempted to simply scrape off the mold, the mold's roots (hyphae) can penetrate deeper into the kimchi than what's visible on the surface. These roots can spread throughout the batch, potentially contaminating the entire container.
Different colored molds (green, blue, black, pink) can indicate different species, some of which can produce mycotoxins that are harmful if ingested. Because you can't easily identify the mold type at home, it's safest to err on the side of caution and discard the entire batch. Food safety experts generally advise against consuming food with visible mold unless it's a mold-ripened cheese or other intentionally moldy product.
To prevent mold growth in your kimchi, ensure it's always submerged in its brine. Press down on the kimchi regularly to release any trapped air bubbles and keep it submerged. Store it in an airtight container in the refrigerator at a consistent temperature.