On the surface, this looks like an excellent idea - give customers a discount if they tweet or like your product on social media.
Unfortunately there are a few problems, both social and technical.
1) Many people have fake twitter and facebook profiles that they use just for discounts like this. They also use those fake profiles to enter contests, sweepstakes, etc. This is far more common that you'd think.
2) Immediately deleting the shared post. I've noticed that many customers will take advantage of the discount and then delete the post on twitter or FB within seconds.
1) There is very little documentation available on how this system works with woocommerce. The 'support forums' are only filled with feature suggestions. There are no actual discussion forums, no knowledge-base, and only a few 5 star 'perfect' reviews. Logic will say that this is certainly odd.
2) Security concerns - this integration gives ShareYourCart complete access to your woocommerce system. They could easily be accessing all of your customers address and payment information. I'm not saying that they are, but you are giving access to your woocommerce system and data.
3) Data mining - ShareYourCart is gathering a gold mine of customer data when you use their system, yet they are charging you for more than 10 uses per month?
I don't have a better plugin suggestion at this time - Share Your cart could be fantastic, but with the system as it is, the security and social concerns are far to great to trust it.
You would be better off asking your customers to tweet and like your product in an email directly to them or in your confirmation email signature.