Looking at the drain setup I believe it's the cause of the slow drain.

It has 2 J-Traps, is this the wrong setup? Is it the cause of the slow drain?

http://i675.photobucket.com/albums/vv116/stevelach1/IMAG0218.jpg

Double trapping is against the plumbing code since it basically converts a P trap to an S trap. When the second trap drains it can siphon the first trap. As to whether it is the cause of your problem -maybe.