bathroom venting plan review
IANA plumber, but I just did similar work in my basement.

A few possible issues I see:

1) Many backwater valves require a certain length of straight, undisrupted pipe flowing into it to ensure smooth flow of water over the valve.  In my case it required roughly 2 feet on the upstream side.  Not the immediate 90 you have. 
 "No branch take-offs may be made closer than 2 feet upstream of backwater valve to insure the smooth (laminar) flow of effluent over the gate of the valve." (from http://www.backwater-valves.com/Backwater-Valve-Installation-Sticker.asp )

2) In my area, at least, any section of drain that is on a toilet cannot also be used for a wet vent of another fixture.  My first inspection failed on this point.  So by that requirement, your shower doesn't have an adequate vent.  If you connected the lavatory drain to the shower line before the toilet, it should be ok.

3) Maybe it's just an assumed detail omitted from your drawing but washing machines need a P-trap and a stand pipe (above the washing machine overflow level).

And as an aside, think about your future self having to frame all of this when you are running your above-slab pipes. :)