FLC OF AN MLG OVERSHOT THEIR ASSIGNED ALT DURING THE INITIAL DEP CLB. THE RPTR STATES THAT THE INCORRECTLY SET ALT WAS MISSED DURING THE TKOF CREW BRIEFING. WHEN THE ACFT WAS LEVEL AT AN ALT 1000 FT HIGHER THAN ASSIGNED; THE CTLR INTERVENED.

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ACFT SET UP FOR CAPTURING DEP (SID) ALT OF 4000 FT AT THE GATE PRIOR TO PUSH BACK. SOMEHOW; BTWN TIME IT WAS SET TO 4000 FT AT GATE AND PRIOR TO TKOF; THE ALT WINDOW WAS EITHER CHANGED TO 5000 FT BY BEING BUMPED; OR IT DID IT BY ITSELF. ON DEP (TKOF) BRIEFING I REMEMBER SAYING 'RWY HDG TO 5000 FT (ETC).' I BELIEVE I SAID 5000 FT BECAUSE THAT'S WHAT I LOOKED AT IN THE 'ALT SET' WINDOW AND IT WAS ALREADY SHOWING 5000 FT AT THAT TIME. NEITHER CAPT NOR I CAUGHT THE FACT IT SHOULD HAVE BEEN 4000 FT. ON CLBOUT; WHEN WE CHKED IN WITH DEP; THE CAPT (PNF) CALLED 'PASSING 3000 FT FOR 5000 FT.' DEP CTLR DID NOT ACKNOWLEDGE; WAS BUSY TALKING TO OTHER ACFT. WE QUICKLY LEVELED AT 5000 FT SHORTLY THEREAFTER. SOMEWHERE ALONG IN HERE; A 'SUPVR' (OR OTHER CTLR) CAME UP ON THE FREQ AND ASKED WHAT WE WERE DOING AT 5000 FT OR WHERE WE'D GOTTEN THAT ALT CLRNC OR ASSIGNMENT. MOMENTS LATER; BOTH CAPT AND I REALIZED THE ALT CAPTURE WINDOW HAD BEEN ACCIDENTALLY OR INADVERTENTLY SET TO 5000 FT BY MISTAKE. LAST LEG OF A LONG (5 LEG) DAY. NOT AS SHARP AS WE NORMALLY ARE; AND PROBABLY HAD SOME 'GET HOMEITIS' CONTRIBUTING TO OUR NOT CATCHING IT DURING THE TKOF BRIEFING.