I have a large pond at least 8 feet deep and quite wide. There are koi and bullhead in the pond, but the pond still seems dirty. We also have two chocolate labs, so I don't want them to get poisoned in any way, but I need something that will clean up the pond efficiently without hurting the fish or the dogs (sometimes there are also geese and ducks that visit).

You may check to see if you have a state or county concervation agent in your area. Often they can come out, or you can take them a water sample for them to check and give recommendations.

Also does this "pond" have a liner or is it more like the farm ponds, where ti is merely dug out in the dirt ?

The geese and ducks are probably the culprits for your dirty pond water. There is nothing worse then goose poo ! You probably can't do anything about that except call wildlife conservation to see if they can give you some tips on how to discourage the geese (ducks aren't bad and are cleaner). There are also water plants you can initiate that keep the water aerated and cleaner.