I have a Wootheme Superstore and Woocommerce, no plugins but add to basket/cart only works sometimes and then independently of the menu mini cart which works intermittently. When a product is added it cannot be removed by the red cross and only sometimes by updating the cart. If you can get to the checkout, the products are actually there though.
I have tried it in all browsers and none work EXCEPT one, Opera and for some reason that works perfectly.
Grateful for some advice as it was all OK before updating Woocommerce (I have raised a Woothemes ticket as I paid for this theme but nobody responds - not a good omen!)