The approval system in Member's Journal and Editor's Pick is basically so we can control what kind of stuff gets posted in there, i.e. posts of a higher quality/calibre, like journal articles. It's a real good way to keep the spammy stuff and trolls from clogging up those sections as well.
On the approve posts page we get a little preview of the post and who wrote it. I'm not sure about other mods, but I generally just briefly skim over that snippet before approving it (or deleting it in the case of spam, etc). We don't spell check (I already reluctantly do this when marking essays for a professor at school, lol), that's left up to you
