Yes, I'd recommend submitting your application at least a few days before the deadline for the reasons you outlined. (I didn't follow my own advice and I submitted it on October 31. Fortunately, I didn't have any problems.)
According to the OLSAS FAQ, there should be a "Document Tracking" feature in your account where you can track which transcripts and other documents have been received and processed.
Every parent I know admits that they are constantly messing things up and letting things slip between the cracks, either intentionally or accidentally.
Obviously there are things that come up that necessitate long hours at times and work on evenings/weekends. But if that's a habit, it means a lot of your work is going to be consistently sub-par, either in terms of quality or productivity.