Wash hands, wash hands, wash hands! That's my biggest thing. Wash hands when you get there, wash hands between dogs if possible, and wash hands when you leave for sure. I'd also remind them to wear scrubby clothes and athletic shoes and not sandals (this sounds like a duh but you never know) as I've gotten both rabbit and dog blood on me (from clipping their nails and them moving their paw too fast), had holes scratched in a shirt from rabbit claws as well as getting it caught in the kennel runs scooting in and out, and getting my clothes totally soaked after giving numerous baths.
I don't know if your shelter does any kind of personality profiles on the dogs that the volunteers can fill out or not, but these are VERY helpful for potential adoptees. Even if the dog already just knows sit or doesn't pull like a freight train on a leash, that still tells folks the dog isn't a complete and total basketcase and that it might be worth adopting.
Remind folks that unless they are experienced in doing baths to have two people help lift the dog into the tub with the "calf carry" so they don't throw out their back if it is a raised tub. For baths, do NOT bathe cats in general. :wink: Unless they make a practice of it, but yeah, just my personal opinion.
I also sometimes help the foster and adoption coordinators take good pictures of the dogs for Petfinder. If they let them do this, this is a really really valuable thing because a lot of shelters put up these really bad poorly focused, bad lighting pictures shooting down from the dogs from up above and they wonder why the dog never gets adopted. I've found the best and fasted method for picture taking is to take a 6 foot black nylon leash and a black nylon slip collar or regular collar (less obtrusive in the photos), tie the dog outside to a tree nearby, get a squeaky toy to get their attention, and take them that way. Hopefully less chance of red eye or glare in their eyes and it usually makes them look more friendly when they are interested in the squeaky toy.
If I can think of some more stuff our shelter does, I'll let you know.