It really reminds me of BillMonk (http://billmonk.com - sort of defunct since they haven't renewed their SSL certificate), a project that was the genesis of Obopay back in 2006. It was very similar to split-the-bill and had a strong emphasis on mobile (ahh - remember when having SMS apps was cutting edge). It had notifications, long-term tracking between parties, and several ways to split it for registered users, but also provided easy service for unregistered users. I used it pretty continuously for about a year but ran into two big issues. One - it was difficult enough to SMS in a bill to split evenly, and a pain to itemize the bill even online. I imagine that even as a web app optimized for different mobile devices, this could still be a problem. When you're at the table and trying to figure out the bill, time is key - that means a quick UI and fast latency. The other issue was getting other people to use it. I convinced maybe three friends to use it over the course of that year and none used it for more than two days. It's difficult to get people to use and stick to.

That said, structuring it as a longterm balancing solution for financial "partners" like roommates might be a better model.