Launching on a weekend can get you more notice, but any day mid week means people have a full weekend to work on it. #twentyfourhourshortstory runs monday to tuesday, #finishthestory starts on Wednesdays, I am fairly certain cut off is the monday but people tend to enter early. With that in mind, maybe a thursday or a friday? I never thought much about the best day, but I am often looking for a contest to write for over the weekend ;)
I am fairly rubbish at the consistency myself, but reminder posts seem to help a lot as well :)
I'm thinking along the same lines. If I post on a Saturday, it will likely be mid- to late-morning. That gives people a day and a half on the weekend to write something. People tend to be busier during the week, I think. But I post a contest in the middle of the week, then they have the whole weekend. That's just me thinking out loud.