My wife's grandmother just told us that Petro Vlahos, in his Oscar acceptance speech during the 38th oscar ceremony thanked my wife's grandfather for his technical help. Is there any way to confirm this? Would the clip be online somewhere? Or are there transcripts of the Oscar ceremonies?
The Oscars website has an Academy Awards Acceptance Speech Database with transcripts and video clips.
Unfortunately it currently only covers 1966 onwards. This page suggests other ways of viewing video from Oscar ceremonies:
Watch a video: It may be possible to view a videotaped segment of the Awards telecast at the Academy Film Archive in Hollywood. To inquire about their holdings or to set up a viewing appointment, contact the public access coordinator for the archive at (310) 247-3000, ext. 2332 or firstname.lastname@example.org. Other institutions with video coverage of the Awards ceremonies include the UCLA Film & Television Archive in Los Angeles and the Paley Center for Media, with locations in New York and Los Angeles.
Listen to audio: Audio recordings of the ceremonies, which include some of the Academy's earliest holdings, are a part of the Music and Recorded Sound Collection in the Department of Special Collections at the Margaret Herrick Library in Beverly Hills. To inquire about their holdings or to set up an appointment, contact the library's music and recorded sound specialist at (310) 247-3000, ext. 2236 or email@example.com.
Contact the National Film Information Service: NFIS, a fee-based research service of the Margaret Herrick Library, can transcribe a specific speech for you. Contact information and a description of services may be found on the library's website.
I'm not positive of your location, but if you're ever in NYC you can go to the Paley Center for Media and request a copy to view. I'm not positive if they can actually make you a copy or not, but their library is massive and it works like any public library; you request certain clips by catalog number and you can watch them on a monitor in a cubicle.