Great question. Most commonly the white deposits we see with unglazed terra cotta pots is caused by the build up of mineral salts from the water and fertilizer used on the plants. Since unglazed, terra cotta pots are porous, minerals work their way through the terra cotta pot and collect on the outside of the pots. These can be treated with a water and vinegar mix (3 parts water to 1 part vinegar). To treat, remove the plant and soil from the pot and soak the pot in the vinegar/water mix. After soaking, scrub (brush) off the deposits and then rinse the pots well. After the pots dry you can return the plants to the pots.

  The bottoms of your pots do appear to have a white mold, most probably powdery mildew. This is caused by the presence of high humidity over extended periods of time.  While basically harmless, the best way to get rid of the mildew is to treat with an organic fungicide such as potassium bicarbonate. Again, remove your plant before treating the pots and remember to rinse your pots thoroughly after treatment and allow them to dry before returning your plants to the pots.

  I would try the vinegar/water soak first and then try the potassium bicarbonate fungicide if the vinegar mix does not completely remove the deposits.

  I hope you have a great summer and enjoy your plants.