Ula's "huge back swing" which Henry (Adam Sandler) calls "the stupidest flippin' swing I've ever seen" was inspired by Happy's (Adam Sandler) swing in Happy Gilmore (1996).
"Jocko" was played by Sivuqaq, one of four walruses living at Six Flags Marine World in Vallejo, CA. The three female walruses featured in the film are named Siku, Uquq and Qiluk.
When Henry goes to visit Lucy at the Institute, she says, "I don't know who you are, but I dream about you almost every night." Since she has no memories of anything after the accident, it seems that she could not possibly know that she had dreamed about Henry more then once, but she very likely made note of it in her journal.
What song plays during Henry's dream about Lucy after bring hit with the golf ball?
A
'Slave to Love' by Elan. The complete 50 First Dates soundtrack can be found here with scene descriptions.
Q
Does Goldfield syndrome exist?
A
Yes, but the name is invented by the film. In reality, it's called anterograde amnesia and usually functions differently to in the film. See http://en.wikipedia.org/wiki/Anterograde_amnesia#Symptoms