I didnt see sizes for all the piping on the drawing so I'm going to assume they are all fine..
As long as wet venting is allowed in your area the bathroom group is fine except for the second vanity. Where I'm from you can wet vent a bathroom group, but only one fixture each. So we would have to vent either both sinks or the last sink and the shower. Check your local codes. Not saying it wouldnt work the way you have it, but code requires a little more. I have had inspectors allow me to turn a stack up between sinks, throw in a cross and vent out the top using the common vented sinks as my wet vent. Also, cant tell by the drawing, but all fixtures must come off the same horizontal plane. This means to hit the toilet and shower you must have your wye or combo fitting laying on its side then 90ing up. Cant have your fixtures dumping straight into the top of your branch.
You can tee right off the stack to your trap for the washerbox and vent out of the top. No need to tee, 90, tee for trap, 90, tee back into the stack. Be sure your standpipe coming off the trap is no less than 18" and no more than 30". I usually go about 24"