In the future, I wouldn't recommend updating major plugins right after an update/release. The changelog shows there was:
Tweak - Payment methods and shipping method selection dropdowns on order page
But I am not sure what this means as it isn't quite clear enough to debug. I'll need to send the issue to Kriesi and have him take a look at the exact change.
Additionally, double check that your shipping methods are correct as they might need to be re-saved. Attempting to get an order through all I'm getting is Local Pickup as an option so it could just be the way the plugin is configured and that it needs to be re-done to your needs.
In the mean time, you'll need to revert to 1.6.1 in order to get back the previous functionality with Woo Commerce if the above doesn't help.