FLC OF A CPR CESSNA CITATION; CE550; OVERSHOT ASSIGNED ALT DURING CLB AND FAILED TO FOLLOW THEIR ACTUAL FLT PLAN ROUTING.

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DEPARTED TEB ARPT IFR FLT PLAN; AND ROUTING XA45 HRS WAS CHANGED ON TAXI. AFTER TKOF AND WORKING NEW YORK TRACON LEVEL AT 11000 FT MSL; RECEIVED CLRNC TO CLB TO 16000 FT AND FLY DIRECT TO THE HUO VOR. FO SET 16000 FT AND FLY DIRECT TO THE HUO VOR. FO SET 16000 FT IN ALT ALERTER AND I SELECTED HUO DIRECT IN THE FMS. CLBING THROUGH 12500 FT; ATC INSTRUCTED US TO DSND AND MAINTAIN 12000 FT; CLRNC LIMIT WAS 12000 FT ACCORDING TO ATC. QUESTIONED ATC IF ANY CONFLICT WITH OTHER ACFT OCCURRED AND REPLY WAS NO. APPARENTLY; WE MISUNDERSTOOD THE ALT CLRNC LIMIT OR ATC DID IN FACT CLR US TO 16000 FT. FO READ BACK 16000 FT ON THE READBACK. I CALLED THE TRACON NUMBER AND THEY WERE GOING TO CHK THE TAPE AND CALL ME BACK. AS I WRITE THIS; TRACON CALLED ME AND THE TAPE REVEALED WE WERE CLRED TO 12000 FT AND THE READBACK WAS 16000 FT AND THE CTLR DID NOT RESPOND TO THE READBACK. THE SECOND AREA OF CONCERN INVOLVES NAV. AS I PREVIOUSLY RPTED; THE ROUTING WAS CHANGED ON TAXI AT TEB. OUR DEST WAS OIC (NORWICH; NY). CLRNC AS FOLLOWS: HUO V252 RAGER INTXN V273 TO JOIN V449 DNY-RKA DIRECT DEST. THIS SIT WAS ENTIRELY THE CREW NOT DISCUSSING THE ROUTING CHANGE FROM THE ORIGINAL HIGH ALT RTE CLRNC TO THE LOW ALT CLRNC. WE FLEW OUTBOUND ON V252 SEVERAL MI BEYOND RAGER AND THE CTLR QUERIED US. WE WERE FLYING V252 TO JOIN V449 INSTEAD OF THE ABOVE CLRNC. NO CONFLICT WITH ANOTHER ACFT EXISTED ACCORDING TO THE CTLR. FLC MUST TAKE TIME TO BRIEF NEW CLRNCS BEFORE TKOF.