I can't figure out how to view the DCI record. I want to confirm the store is reporting the games I ran.
Good luck! 
You can log in at https://webapp.wizards.com/personal.aspx but there's not much you can do there. You can't change your name from "Unknown Unknown," for instance. The link to the "latest information on Dungeons & Dragons" gives a 404 File Not Found error. The Judge Center is for card games only. (I think it would be cool to have certification/levels for DMs, like we did in the old RPGA.) And the Planeswalker Points program is for M:tG only.
If you figure it out, please let me know!
The simple answer is you can't, because they're not logging the games in any specific fashion that's viewable to us. At best they're keeping track of the number of games played for statistics purposes.
-HM
The store reporting is only for attendance purposes. If you're running games and want to make sure you're getting your DM rewards you just need to fill out an adventure logsheet, just like a player. Notate that you DMd and record your rewards, that's it.