BE02 FLC COCKPIT COORD FAILURE OCCURRED WHEN ACFT TURNED ONTO RWY WITHOUT DEP WX CRITERIA. WX CHANGES WHILE ON RWY AND FLC IS STILL WORKING DEP TKOF CHKLIST WHILE ACFT BECOMES AIRBORNE. FLC CLBED ABOVE DEP ASSIGNED ALT OF 3000 FT DUE TO COCKPIT DISTRACTIONS ASSOCIATED WITH LATE SCHEDULING PRESSURES.

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MY CAPT AND I WERE CLRED FOR TKOF ON RWY 36 AT OMA. I AM A RELATIVELY SENIOR FO AND MY CAPT RECENTLY UPGRADED AND HAD HIGH MINIMUMS. THIS WAS OUR 3RD DAY TOGETHER. WE TAXIED ONTO THE RWY AND WERE TOLD BY TWR WE WERE CLRED FOR TKOF AND RVR WAS 2000 FT. BOTH MY CAPT AND I COULD SEE AT LEAST 6000 FT DOWN THE RWY. MY CAPT AND I REALIZED WE COULDN'T LEGALLY DEPART. WE STARTED TO SLOWLY COAST DOWN THE RWY. WE BOTH WERE PREOCCUPIED WITH VISIBILITY. I ASKED AGAIN FOR THE RVR. THE TWR REPLIED 2000 FT. THE ACFT BEHIND US WAITING TO DEPART ASKED TWR WHY THEY COULD SEE TO THE END OF THE RWY. TWR REPLIED THE RVR EQUIP MUST BE BROKE. I KEYED THE MIKE AND ASKED FOR PREVAILING VISIBILITY. 2 MI WAS THE REPLY. WE COULD NOW LEGALLY DEPART. WE HAD COASTED AT LEAST 1500 FT DOWN THE RWY. OUR PRE-TKOF CHK HADN'T BEEN DONE AND AS WE ADDED PWR; I COMPLETED THE CHK JUST BEFORE ROTATION. BOTH OF US WERE BEHIND THE ACFT DESPERATELY TRYING TO CATCH UP. TWR GAVE US A VECTOR; TOLD US TO CONTACT DEP AND CHK OUR XPONDER. OUR DEP CLRNC SPECIFIED A 3000 FT DEP ALT. THE ACFT QUICKLY GAINED THE 1500 FT AS WE WERE TURNING; CLBING; IMC; CONTACTING DEP; AND COMPLETING THE AFTER TKOF CHKS. TOO LATE; I NOTICED THE ALT WAS 1000 FT TOO HIGH (4000 FT MSL) AND MENTIONED IT TO THE CAPT WHILE DEP WAS GIVING US INSTRUCTIONS. HE DIDN'T CORRECT; SO I PUSHED THE NOSE OVER. BY NOW WE WERE 1300 FT HIGH (4300 FT MSL). WE QUICKLY LOWERED THE NOSE AND DSNDED DOWN TO 3000 FT MSL. DEP INQUIRED ABOUT OUR ALT AS WE WERE CORRECTING IT. FORTUNATELY; WE RECEIVED NO TCASII OR ATC ALERTS; AND THE FLT CONTINUED UNEVENTFULLY. OUR PROB WAS CAUSED BY A RUSHED TKOF IN MARGINAL WX AFTER WE WERE BOTH DISTRACTED. NEITHER OF US SHOULD HAVE ALLOWED THE TKOF TO CONTINUE. WE SHOULD HAVE TAXIED OFF THE RWY WHEN THE QUESTION OF VISIBILITY MAY HAVE PREVENTED OUR DEP AND QUESTIONS ABOUT VISIBILITY OR POSSIBLE RVR EQUIP FAILURE COULD THEN HAVE BEEN ADDRESSED ON THE GND. WE WERE TOO CONCERNED WITH TIME SCHEDULES FOR AN ALREADY LATE DEP. A FEW MORE MINS ON THE GND WOULD NOT HAVE MADE ANY DIFFERENCE OVERALL AND WOULD HAVE ALLOWED US TO CALMLY EXAMINE OUR SIT AND DETERMINE A SAFE AND LEGAL COURSE OF ACTION.