How do you know if molds or bacteria that you have cultured in a petri dish are dangerous?

Answer from a Biosafety Officer:

June 10, 2013

The most straightforward answer to your question is that you can’t tell whether a culture of bacteria is "safe" or "dangerous" just by looking at the appearance of colonies on a plate.  Colony morphology (the shape, color, and general appearance of a bacterial colony on a plate) is one aspect of bacterial identification and can be used as a step in identifying the cultures on your plate (1).

For this reason, biosafety guidelines recommend using Biosafety Level 2 (BSL-2) practices and facilities when working with samples that contain unknown microbes, and therefore unknown hazards (2:  Section II:  Biological Risk Assessment; 3:  Isolation of Unknown Microbes from the Environment).

References:
1.     Breakwell, D., Woolverton, C., MacDonald, B., Smith, K., and R. Robison.  Colony Morphology.  ASM MicrobeLibrary.  http://www.microbelibrary.org/component/resource/laboratory-test/3136-colony-morphology-protocol.  Accessed 03/01/2013.
2.     Wilson, D., and L. Chosewood, editors.  Biosafety in Microbiological and Biomedical Laboratories (BMBL), 5th edition.  Centers for Disease Control and Prevention and National Institutes of Health.  2009.  http://www.cdc.gov/biosafety/publications/bmbl5/.  Accessed 03/03/2013.
3.     American Society for Microbiology.  Draft Guidelines for Biosafety in Teaching Laboratories.  2012.  http://www.asmcue.org/documents/ASMBiosafetyGuidelines-v2.pdf.  Accessed 03/03/2013.