WHILE RTRNG TO SANTA MONICA (SMO) FM A X-COUNTRY, THE PLTS DIVERTED TO VAN NUYS WHEN THE RWY AT SMO WAS CLOSED DUE TO A DISABLED ACFT. AFTER THE RWY WAS REOPENED, THEY FILED AN IFR FLT PLN TO CONT AT 5000' & TKOF AT NGT. DRG DEP, THE AR-3 CTLR PROVIDED RADAR VECTORS (FOR CLNC AT 3000'). AT 1926:39, AR-4 CTLR ACKNOWLEDGED/ACCEPTED AN AUTOMATED HANDOFF VIA AN ARTS-III COMPUTER KEYBOARD ENTRY. AR-3 PROVIDED ADNTL VECTORS TO THE FLT, THE LAST BEING A 080 DEG HDG (AT 1929:12), BUT DIDN'T TELL THE PLTS TO CHG TO AR-4'S FREQ. AT APRX 1933, THE AR-3 & AR-4 CTLRS WERE RELIEVED & BGN BRIEFING THEIR RELIEVING CTLRS. SOON THEREAFTER, THE FLT PASSED OVR THE ASR ANTENNA, THEN WAS DISPLAYED ON THE RADAR SCOPE IN A COAST MODE. IT REAPPEARED WITH A DATA TAG, THAT ERRONEOUSLY INDCD ANOTHER FACILITY HAD CTL OF THE FLT. THE RELIEVING CTLRS SAWTHE FULL DATA BLOCK ON THEIR SCOPES, BUT DISREGARDED IT, DUE TO THE ERRONEOUS CTL SYMBOL. SUBSEQUENTLY, THE ACFT HIT MTNS AT THE LAST ASSIGNED ALT OF 3000'. THE CFI HAD JUST MOVED FM FL TO CA & WAS ON HIS 2ND DAY OF EMPLOYMENT IN CA.