MDT CREW WAS CLBING TO FL270 WHEN THEIR CLRED ALT WAS FL250.

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ACR X FROM YYZ TO PHL; WITH ZOB WHO HAD ASSIGNED FL270; AND WERE CLBING OUT. BOTH PF AND PNF CALLED OUT 'FL270.' FLT ATTENDANT CAME TO FLT DECK TO RPT ON SICK PAX (BUMPY). CTR CHANGED FREQ WHILE I WAS OFF AND FO CHKED IN. CTLR ASKED ASSIGNED ALT. FO ANSWERED 'FL270.' CTLR THEN SAID 'FL 250' WAS ASSIGNED ALT. FO STOPPED CLB AT FL258. CTLR ASKED IF WE WANTED FL270. FO ANSWERED 'YES' AND CTLR ISSUED CLB TO FL270. NO TFC IN AREA. CONTINUED NORMAL OPS. CONTRIBUTING FACTORS: 1) LAST TRIP OF 4-DAY SCHEDULE. 2) LATE NIGHT FLT OUT OF UNFAMILIAR CITY (CANADA). 3) NUMEROUS PROBS WITH CTLRS AND CREW MEMBERS ON NEW FLT NUMBERS (SERIES). PREVENTION: 1) CURRENT OP PROCS SHOULD PREVENT ALT EXCURSIONS. AFTER PNF READS BACK ASSIGNED ALT TO ATC; PF SETS ALT IN FLT CTL PANEL AND VERIFIES IT. PNF RE-VERIFIES THE DISPLAYED (ASSIGNED) ALT. 2) NUMEROUS MULTI-NUMBERED FLTS WITH SIMILAR CALL SIGNS ARE A DETRIMENT TO READBACK/HEARBACK PROBS. SUPPLEMENTAL INFO FROM ACN 598862: CAPT TOOK RADIO CALL FROM ZOB TO CLB TO FL270. I READ BACK FL270 AND ASKED WHAT ALT WE WERE CLBING TO. I ANSWERED THE CALL AND STATED FL270. CTLR STATED THAT WE WERE ASSIGNED FL250; THEN ASKED IF WE WANTED TO CONTINUE ON TO FL270. I SAID YES. HE SAID 'CLB TO FL270;' AND CONTINUED NORMAL OP. THE CAPT WAS ALSO TALKING TO THE FLT ATTENDANT ABOUT A SICK PAX. IT WAS THE LAST LEG OF A 4-DAY TRIP AT NIGHT. AS PF; I UNDERSTOOD THE PNF REPEAT FL270. I STATED FL270 AND SELECTED IT IN THE AUTOPLT AND WAS CLBING TO FL270. IF FL250 WAS WHAT WE WERE ACTUALLY ASSIGNED; SOMEWHERE THERE WAS A MISUNDERSTANDING. WE SHOULD BE MORE ALERT FOR ATC INSTRUCTIONS; AND RE-VERIFY THEM WITH EACH PLT.