Here some information from American Film Institute (DV= Daily Variety)
The 31 Jul 1962 DV reported that producer Ted Richmond had recently returned from New York City, where he selected twelve songs for the picture from the offerings of seventeen songwriting teams. One month later, the 31 Aug 1962 edition *** noted that Presley had pre-recorded eight of the compositions, including the title song.
On 4 Sep 1962, DV announced that the 200-member cast and crew were leaving for Seattle, WA, to begin production the next day. Director Norman Taurog and director of photography Joseph Ruttenberg scouted locations several weeks earlier, as reported in the 15 Aug 1962 edition. The 11 Sep 1962 DV stated that composer Leith Stevens left for Seattle that day to supervise the musical finale.
According to the 9 Oct 1962 LAT, four mobile homes, constructed by Divco-Wayne Industries, were delivered to MGM Studios in Culver City, CA, for a trailer park set on Stage 20. The article claimed that it was the first time mobile homes were depicted on screen in a "deluxe park setting." The 26 Oct 1962 DV noted that a replica of Seattle's "Space Needle" building was created for the film.
After the company returned from Seattle, the 16 Oct 1962 DV reported that Norwegian Vice Consul Arild Riisberg appeared on set the previous day to present Elvis Presley with a "silver record mounted on a mahogany plaque," on behalf of the people of Norway.
As both production and the Seattle Century 21 Exposition drew to a close, the title of the picture was changed to It Happened at the World's Fair, as stated in the 23 Oct 1962 DV. Filming concluded on 8 Nov 1962, according to that day's issue. News items in the 17 Jan 1963 and 6 Feb 1963 editions of DV reported the start of recording the music score and the completion of music dubbing, respectively. Meanwhile, RCA Victor shipped more than 516,000 copies of Presley's latest single, featuring two songs from the picture. A news brief in the 28 Jan 1963 DV revealed that a preview screening was held in Long Beach, CA, over the previous two days.
On 8 Apr 1963, DV announced that the picture was opening that week at 450 locations, supported by a "heavy" radio and television campaign targeting the teenage demographic. It Happened at the World's Fair opened 3 Apr 1963 in Los Angeles, CA, and on 29 May 1963 in New York City to dismissive reviews, with the 1 Apr 1963 DV and 6 Apr 1963 LAT both describing the picture as "tedious." Regardless, critics predicted a profitable run, evidenced by earnings in Los Angeles of $125,000, as reported in the 9 Apr 1963 DV.
*** now we know this information is wrong; in the pre-selection on 24 august 1962 9 songs were selected according to the acetates with demo versions.