Whenever I have a glut of citrus fruits I like to grate the peel to use in recipes later. I dry the grated peel on a cookie sheet then put it

gosh, adianne, I hate hearing that you dry your citrus zest. For me, who is a real citrus 'freak' , drying takes out all the bright punchy flavor that makes citrus zest so special! I have 2 suggestions:
1) if you have freezer space, peel the citrus with a vegetable peeler- in wide strips- and freeze those. Then, if you want to add fine zest to baked goods, etc., use a micro-plane to zest the frozen strips, or just finely mince the strips by hand.
2) if you have too much citrus to fit in your freezer, and you like sweets, then candy a batch of the citrus peels. These can then be stored in the frig or freezer or on a dark shelf and later eaten as is; or chopped to add to desserts, or dipped in chocolate and eaten or stored or given as precious gifts!

Okay - one more (hopefully last!) thought: if the zest really is completely dry (like after dehydrating) you still need to "condition" it. Conditioning occurs after you put it in the jar. For the first week that you store it, you need to give it a good shake once a day. After that, you should have no trouble with sticking. Conditioning is required for all fruits/veggies that you dehydrate.

One more option -- you could consider using strips (instead of grated zest) and candying it. I am particularly fond of candied orange peel :)

You might try freezing the zest -- works really well (that's what I do). Alternately, if you want to dry it, use either a food dehydrator or oven super low (about 160 degrees -- some ovens don't go that low) for several hours. Retained moisture like you are describing is a breeding ground for mold.

It might be worthwhile to try putting a silica packet (I don't know of a source, but you could use one that came with another food) into the jar to see if that helps. Another option would be switching to freezing dots of the grated peel instead of drying it.