I wanted to make sure it was wrong before talking to my landlord.
That's what we're here for. I'm guessing your landlord did this himself or hired a handyman to do it. Just because the pieces fit together doesn't mean it is correct.
Here are a couple of plumbing guides for homeowners that we like and you may find interesting.
http://www.klickitatcounty.org/documentcenter/view/103
Helpful Plumbing Hints for Residential Construction by Bert Polk Plumbing Inspector Lincoln County
The second guide is by Bert Polk, a highly-regarded plumbing inspector, and the photos in his guide show how it looks when good plumbers do their work correctly and in compliance with the building code. Maybe a little advanced, but very well done.
By the way, in your photo, I don't really see where sewer gas would be escaping out of the sides of the pipes or at the pipe connections themselves, but it is I guess possible that with the Y at the end there, one drain might be siphoning the P-trap of the other, and gas could be rising from the sink drain. (The P-trap is the U correctly done on the non-disposer sink in your photo that holds water in the bottom of the U and thus blocks sewer gas from flowing up the drain; the water in the trap provides a seal against gas coming up through the sink drain into your kitchen). You say you don't use your disposer but you probably do use your dishwasher, the drain of which is connected to your disposer. Modern dishwashers don't produce a huge jet of water when pumping out the way our old Maytag dishwasher did, but I guess it could be enough of a rush when it hits that Y at the wall that it could siphon the p-trap of the non-disposer sink drain and thus be the cause of what you are smelling. And maybe vice-versa depending upon how you use your non-disposer sink. It could well be something else, but that's the most obvious possibility -- and is one reason why the disposer is normally hooked up in a dual-sink the way the Lowe's guy does it. I would give each drain opening in your sinks a good sniff and see which (if any) of them has a gassy smell.
