If you decide to date someone who is not a Christian, you will certainly come across opinions and viewpoints different from your own. This could serve to widen your perspective and cause you to examine your own beliefs. At the same time, these different viewpoints may bring you into conflict as a couple, so be aware that the relationship may take more work than if you were dating a fellow Christian.
This is the most-often touted pro for a Christian dating a non-Christian. The idea is that over time the Christian could persuade her non-Christian partner to become a believer. While this is certainly theoretically true, and does happen on occasion, oftentimes the opposite occurs--a believer will either leave the faith for her partner, or dilute her own beliefs to compromise for the sake of the relationship.
A Wider Circle of Influence
Dating a non-Christian will bring you into contact with other non-Christian individuals through your significant other's friends and family. This could, in theory, make you more effective in opening more peoples' hearts to Jesus. Most of the time, though, the strength in numbers prevails, and a Christian will either stay quiet about his faith or give it up entirely in this situation.
Spending lots of time with people outside of the church will make you more aware of trends and secular culture. This could possibly make you more effective in your witnessing at present or down the road. If you can find a way to present the gospel effectively in this environment, it will help both you and them in the long run. This level of knowledge can also be derived from other means, such as following the news or interacting with people on the Internet.