No reason for him to know about any details of the mystery. If you are trying to build a long comprehensive plot together (sometimes nice, but not necessary) you will have to discuss that of course.
The only other worry would be making sure you are both in agreement about the level of treasure given out and stuff like that. If you depart much from the WBL guidelines that can have quite an effect on challenge ratings.
As long as you're DMing different adventure locales, you don't really *need* to pass on much information to a rotating DM. Unless you're the kind of DM who keeps many things secret, like magic item properties and such. Sure, there will be less continuity, fewer opportunities for recurring villains, and far few long-term links between adventures DMed by different people.
Although you could orchestrate some cool effects by passing along select bits of secret info... as long as the other rotating DMs are cool with RPing a lack of knowledge about certain things.
We've been playing the former system for some 4 years in a DD3.5 campaign. Never tried the latter. Just saved up campaign secrets and recurring villains until our next DM slot came round. Also, we simply revealed magic item properties and had the players assess the 100gp cost to identify (DD3.5, remember?). Now, that would be even less problematical as long as a player is a spellcaster with high spellcraft, or the group has access to such an NPC.