I salivate a lot at night, and my teeth are whitening unevenly. Are they related, and what should I do?

Two problems: the trays are causing me to salivate a lot at night (sometimes I'm almost drooling, though I go directly to bed after putting them in, and lie on my back); my teeth are definitely whitening, but darker toward the gums. I'm thinking that maybe saliva is getting into the trays? How can I tell, and what should I do?