DRG THE TKOF ROLL, THE CREW FELT A VIBRATION BTN 135 KTS & LIFT-OFF. THEY LEFT THE GEAR EXTDD & WERE ADZD 2 TIRES HAD SEPD FM THE RGT INSIDE MAIN GEAR TRUCK, A 3RD TIRE BLEW OUT & THE 4TH APPEARED INTACT. THEY DUMPED FUEL & LNDD. AN EXAM REVEALED THE TIRES HAD FAILED, RESULTING IN SKIN DMG & BKN HYD LINE(S). CARGO HAD BEEN LOADED WITH MORE PALLETS ON THE RGT SIDE; SOME PALLETS WERE NOT MARKED TO INDC WT OR SHIPPING ID. A COMPUTER PRINT-OUT (SIGNED BY CAPT & STATION AGENT) SHOWED A LATERAL IMBALANCE OF 18,766 LBS. WITH THIS IMBALANCE, GROSS WT SHOULD NOT HAVE EXCEEDED 744,000 LBS; ACTUAL WT WAS 751,316 LBS. AFTER DEPG THE CARGO RAMP, ACFT WAS TAXIED 3 MI IN A STRAIGHT LINE, THEN 2 LEFT TURNS WERE MADE ONTO RWY 6R FOR TKOF. PREVIOUS LOADING CRITERIA PROVIDED 3% ALLOWANCE FOR RANDOM DISPOSABLE LOADS ON PALLETS. IN 1969, FAA ISSUED AN EXEMPTION FM FAR 25.471(B) TO ALLOW BOEING 747'S TO BE LOADED TO DESIGN LIMIT, PROVIDED INSTRNS WERE AVBL TO ASSURE A SYMMETRICAL LOADING. OF 239 KNOWN TIRE FAILURES, 71 INVOLVED THE FLYING TIGER LINE, AN ALL CARGO CARRIER.