How can i troubleshoot where the problem lies?

I have a booking system to book guided tours. The main domain (php and codeigniter) is at eternalcitytours.com. There is then a subdomain (ruby on sinatra) which contains the product pages booking.eternalcitytours.com

On these product pages there is a booking system where people choose the type of tour, no of participants, date and time, before either adding to basket or beginning the checkout.

HOWEVER, certain (lots of people) cant progress to adding to cart or beginning to checkout - nothing happens on clicking those buttons. My problem is that it works for me, and for others, and i have no way to know or understand who it's not working for or why as i cant reproduce the error.

I think it may have something to do with javascript and timezones but i'm at a loss.

Can someone point me at least in the right direction or advise on how i can troubleshoot this issue please??

thanks