I'm putting in a basement bathroom and working through the drain layout. There is a slab already poured so I want to get it right before busting up the concrete. It will be inspected, basically following UPC code (Oregon). This is my first time doing drains and I'm seeking feedback on the plan.
Can you please look at my plan and let me know any problems you see? Please pick this apart. Sorry if this is not a specific enough question. Thanks. 
EDIT:
I reworked this a little bit more, and most importantly talked with the inspector. I learned in my city they now allow Air Admittance Valves (aka AAV, studor valve, or cheater valve) so the long vent pipe isn't necessary. I just have to have a louvered cover over it on the wall so it could 1) be replaced if it ever fails and 2) draw air into the drain.
Also per the answer below I couldn't have the shower join the drain pipe before the wet vent so that is solved with this second plan.
The particular backwater valve linked in the answer had some specific installation instructions regarding the 2 foot rule. Thats not in the code anywhere and the inspector I talked to hadn't known of the 2 foot rule, and just said get the valve that doesn't have that in the instructions (since instructions must be followed per the code). I picked up a backwater valve without any mention of the rule but still allowed 2 feet of a straight shot into the valve anyway in this redesign.
I'll amend this post if I have any problem with the inspection, but so far so good.
NEW PLAN:
Best Answer
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. :)