Moe is a mild shedder, but last summer we went through a few weeks when he was shedding so much that I was afraid he had a serious health problem. A trip to the vet revealed that, nope, he was just shedding. I swear he must have lost every hair on his body in those few short weeks. Never, in all his eight years, did he shed so much. But it was only bad that one time.
Also, we are one of the lucky ones who have never had to worry about anal glands. Only one time, right after surgery to remove some cysts, did we have to have his anal glands expressed. My uneducated guess on the cause was that anesthesia drugs and/or the stress of the event affected his system, slowing it down or something. He began to act uncomfortable and to lick at the area. Once expressed he was back to his normal self in no time at all and has been fine since.
Moe's relatively dry-mouthed in that he doesn't drool much, except when we walk him. New and interesting smells, like we encounter outside of our own yard, seem to cause the infamous Basset slobber to start. Very gross, especially when the slobber is coated in dirt and leaves. We keep slobber rags - or Moe-rags - around to wipe his mouth. I cut up old bath towels into quarters for this. It's possible that your Basset may be dry-mouthed too, but even "dry-mouthed" Bassets "leak" when they drink.