CORP G4 ACFT HAS DIFFERENTIAL SPDS BTWN CAPT AND FO INSTS. COMPUTERS NOTICED THE ERROR AND WARNING LIGHTS ILLUMINATED. AUTOTHROTTLES DISENGAGED. WITH ALL THE CONFUSION THERE WAS AN ALTDEV AND SPD DEV.

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AUTOTHROTTLE TKOF. DURING TKOF ROLL; PASSING THROUGH APPROX 100 KIAS AIRSPD; DIFFERENCE NOTED BTWN CAPT AND FO AIRSPD INDICATORS. AS AIRSPD INCREASED THE DIFFERENCE BTWN THE 2 SYS BECAME LARGER. PNF CALLED V1 PRIOR TO ANY RESOLUTION. AT THAT TIME CAPT AIRSPD INDICATED APPROX 100-110 KTS AND FO AIRSPD INDICATOR INDICATED 120-130 KTS. STANDBY AIRSPD INDICATOR AGREED WITH FO AIRSPD INDICATOR AND FMS GND SPD FAVORED THOSE 2 ALSO. PNF CALLED ROTATE AT VR AND ACFT ACCELERATED THROUGH V2 BEFORE PF INITIATED ROTATION. ACFT CONTINUED TO ACCELERATE RAPIDLY IN CLB ATTITUDE. PF CALLED FOR GEAR AND FLAP RETRACTION WHICH WERE ACCOMPLISHED BY PNF AND RPTED UP. SHORTLY AFTER LIFTOFF AS AIR DATA COMPUTER SENSED AIRSPD DIFFERENCE; THE AIR DATA COMPUTER MISCOMPARE CALIBRATED AIRSPD ILLUMINATED; THE YAW DAMPER INOP CALIBRATED AIRSPD ILLUMINATED AND THE YAW DAMPER DISENGAGED AND THE ELEVATOR TRIM INOP CALIBRATED AIRSPD ILLUMINATED AND THE ELEVATOR TRIM DISENGAGED. ALL OF THIS OCCURRED ALONG WITH THE AUTOTHROTTLES DISENGAGING. WITH ALL OF THESE CAUTIONS AND THEIR ASSOCIATED CHIMES; THE AUTOTHROTTLES DROPPING OFF; THERE WAS A GREAT DEAL OF ACTIVITY; INCLUDING IMC; ALMOST IMMEDIATELY AFTER TKOF. PASSING THROUGH APPROX 1500-2000 FT THE PF GAVE CTL OF THE ACFT TO THE PNF. ON DEP THE SID CALLS FOR LEVELOFF AT 2000 FT WITH THE ASSOCIATED AIRSPD BEING 200 KIAS. WELL; WE MISSED BOTH OF THOSE. DURING THE CTL TRANSITION THE ACFT ALREADY AT 260 KIAS AND CLBING THROUGH 2000 FT REACHED; 2400 MSL AND GRADUALLY SLOWED BACK TO 200 KIAS; THEN DSNDED TO 2000 FT MSL. AT ABOUT THAT TIME WE CALLED DEP WHO HAD BEEN WAITING FOR US. THEY GAVE US A CLB AND A VECTOR TO ON COURSE. THE AIRSPD PROB REMAINED FOR APPROX 20 MINS THEN WENT AWAY RESTORING ALL SYS. CAUSE: ACFT HAD BEEN WAXED THE DAY BEFORE AND MELTED; BURNED WAX RESIDUE WAS FOUND IN THE CAPT'S PITOT TUBE BY MAINT ON POSTFLT. WE WERE NOT PREPARED FOR THIS ANOMALY; STRUGGLED THROUGH IT; BUT NOT WITH THE PRECISION WE NEEDED. CREW SPENT 40 MINS DEBRIEFING THE EVENT AT THE DEST ARPT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THE COMPANY HAS TAKEN PRECAUTIONARY STEPS TO AVOID A REPEAT OF THE INCIDENT. THE PEOPLE WHO WAXED THE ACFT HAVE BEEN ADVISED OF THE INCIDENT AND EDUCATED SO THEY WILL COVER THE PITOT TUBE IN THE FUTURE. THEY USE A MELTED; BURNED WAX AND RPTR BELIEVES THE WAX ACCUMULATED ON THE EDGE OF THE BUFFER AND SPILLED OVER INTO THE PITOT TUBE ACCIDENTALLY.