Dried seaweed is rich in mineral salts and contains very little available moisture.  This combination inhibits growth of bacteria, yeast, and molds, and ensures a prolonged shelf life of at least 3-5 years if the seaweed is kept properly stored. Recommended storage containers are our re-sealable bags or, for bulk amounts, glass jars with screw top lids. Refrigeration is not necessary or desirable, because it can contribute odors and moisture to dried seaweed.  Room temperature storage in a closed cupboard or on the counter but away from direct sunlight is fine.
Sea veggies exposed to moisture or excessive heat may show signs of mold or deterioration. This will be readily visible as discoloration, and the seaweed may have an off-odor similar to mushrooms or seafood past their prime. The whitish powder that sometimes appears on sea vegetables consists of precipitated salts and sugars.  These add flavor and saltiness to the seaweed and it remains safe to eat. You can rinse or use as is. It is not a good idea to rinse sea veggies and store unless you're going to use in 24-48 hours or refrigerate.
If your sea veggies get too dry and crispy, they can be rehydrated by adding a piece of lettuce, slice of apple or damp paper towel to the container for a day or two. Brittle kelp or Alaria can be lightly sprinkled or soaked until rehydrated to your preference.