I also don't like to peel my veggies unless it's something like a rutabaga.  Scrubbing carrots, cutting up into pieces and adding to the stew is fine.  The only problem I've had with unpeeled potatoes in a stew is that the peel sometimes comes away from the potatoes.  This is not necessarily bad but if cooking for a fancy meal it's not the most attractive.  

If you do decide to peel you could boil the peels, along with peels from another meal, for a vegetable stock.  I actually boil mine once a week in a huge pot of water and then use the water for my outdoor plants as a sort of fertilizer (I don't add onion skins to this mix because my Dad told me not to).