Being someone who submitted an application around 11:59pm in a previous season, I wonder what makes people wait until the last minute. In our case it was the big decision of whether we should apply or not (we didn't have a site, didn't really talk it through among ourselves), which pretty much made the resulting rejection a self satisfying prophecy.
Are you ever really done with something like this? There's always something you could improve, given more time. Using all the available time makes sense.
I believe that the best time to start is right now.
PG has said, many times, that he's more interested in the team than the idea.
A solid team isn't really going to change that much over a few months, as they've probably known each other for years. Show that in the interview, and you'll have a better chance of getting at-bat with YC than a few months of polish on your startup.
On top of that, showing real progress between submitting your YC app and actually talking to YC speaks worlds about your ability to execute, far more than having a polished last-minute entry.
