A B737 FLT CREW DEPARTED WITHOUT A REQUIRED ALTERNATE IN THE DISPATCH RELEASE.

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TKOF CONDITIONS AT OMA WERE 1/4 MI VISIBILITY AND LIGHT WINDS. THE CAPT NOTICED THAT THE TKOF ALTERNATE DESIGNATED BY DISPATCH WAS GREATER THAN 300 MI AWAY. THE TKOF ALTERNATE WAS ALSO OUR DEST. IT TOOK WAY TOO LONG TO CONVINCE THE DISPATCHER THAT THE ALTERNATE DIDN'T COMPLY WITH THE FAR'S (LESS THAN 300 MI IN STILL AIR). A SUITABLE ALTERNATE WAS SELECTED AND THE RELEASE WAS AMENDED. THIS PROCESS LASTED UNTIL MOMENTS BEFORE PUSH TIME. I WASN'T IN ON THE DISCUSSION BECAUSE I WAS PERFORMING MY ORIGINATING PREFLT DUTIES. WHAT BOTH OF US FAILED TO NOTICE WAS THAT WE NEEDED A LNDG ALTERNATE ALSO BECAUSE OF THE CEILING AT MDW. THE RELEASE DIDN'T SHOW A LNDG ALTERNATE AND SHOULD HAVE. THE CAPT HAD THE WX PACKAGE WHILE TALKING TO DISPATCH; SO I NEVER GOT A CHANCE TO LOOK AT IT UNTIL MOMENTS BEFORE PUSH AND DIDN'T NOTICE THE MDW WX. I WAS FOCUSED ON THE TKOF ALTERNATE SIT. I FEEL THAT THE DISPATCHER WAS TRYING TO BE A LITTLE TOO EFFICIENT. WHILE A TKOF ALTERNATE THAT IS THE SAME AS YOUR DEST MAY SOUND GREAT IN THEORY; IT STILL HAS TO COMPLY WITH FAR'S. THE CAPT HAD TO SPEND WAY TOO MUCH TIME TRYING TO CONVINCE DISPATCH OF THIS. WE GOT IN A RUSH TO GET OUT ON TIME AND DIDN'T REVIEW THE REST OF THE DOCUMENT. THE CAPT DID GET MORE FUEL BECAUSE OF TKOF CONDITIONS (1/4 MI VISIBILITY); SO WE WERE SAFE TO GO TO AN ALTERNATE; BUT THE PAPERWORK WAS NOT CORRECT. I KNOW TIMES ARE TIGHT AND FUEL IS EXPENSIVE; BUT WE CAN'T CUT CORNERS LIKE THIS. DISPATCH NEEDS TO ADMIT THEIR GREAT PLAN MAY NOT BE SO GREAT AND FIX IT FAST. WE; AS THE CREW; SHOULD NOT HAVE BEEN SO FIXATED ON THE ONE PROB AND SEEN THE BIG PICTURE.