First off, nice humi!
If you have small cracks, seams, etc.. that need to be sealed up I would just go ahead and seal them with the clear silicone/aquarium caulk. Do it while you still have it outside to it can air out and dry quickly. The smell wont stick around forever but you definately don't want your stogies picking up that awful odor.
For the doors and moving parts I would try to use some type of weather stripping. Like the others mentioned, some breathing is ok to have but obviously you don't want your humidity fluctuating up and down.
Make sure you get some circulating fans for that beast!