heh, you're doing a lot of shit wrong there, at least as far as the code I'm used to goes. T's or TY's are not supposed to be used on their backs, for one. Only on the vertical. But that's not really a big deal. Your toilet isn't vented, near as I can tell, nor is the standpipe for your washer. When your toilet flushes it will probably pull the water from the laundry trap. If you extended a vent from your washer stand pipe to tie in to the other vent, then that would vent both the washer standpipe and the toilet. Same goes with the sink and dishwasher upstairs, those need to be vented.
Basically the whole concept of DWV is to make sure that any traps are protected by a vent. If they aren't then they can be siphoned off either by momentum from that fixture, or by another fixture downstream. No trap seal results in sewer gas leaking directly in to the building, which is mostly a nuisance but can also be lethal if it's really bad gas with CO. Or can result in an explosion if there's a bunch of methane.