You're right to be concerned about this. As with any rodent, a squirrel may have ingested any number of toxins (including rat poison), which will do the same thing to your dog as it does to the rodent if he ingests it. It might not look like it for a while, but if this is something he does a lot, it will build up, along with the symptoms and side effects. By the time you notice, he could have severe and terminal liver damage.
There's another threat is Hepatozoonosis. This is a tick borne disease that occurs in dogs after they ingest the tick rather than the tick attaches to the dog as we normally see happen. Squirrels are known to be pretty good carriers of ticks (and fleas and other parasites) which can be mild to lethal problems for your dog.
http://www.addl.purdue.edu/newsletters/2003/Spring/ACH.shtml (more about hepatozoonosis)
Fleas on the squirrel may also infect your dog with tapeworms and a host of other intestinal problems that he might not otherwise be exposed to.
These are a just a few of the more obvious problems with him eating these rodents - hopefully enough for you to encourage him not too.
You might have better luck eliminating the squirrels from your yard. They come for seeds, nuts and whatever else they can find - so if you have bird feeders there - either pull them or make the seed distasteful for the squirrels by adding lots of hot pepper flakes. Birds don't perceive capsaicin the way mammals do so it won't stop their feeding, but will curb the rodents.
A water guard like "The Scarecrow" is a motion triggered watering device that may also help.
Giving your dog some negative reinforcement like a loud noise (clap of the hands, rattle of a can with pebbles or coins in it) or squirt of water to her hind end - may also help.
it's a difficult situation. Mostly I'd try to eliminate the squirrels reason for being there (the food source).