Audio problem: Hamlin Rule, the bad guy in this episode, is a singer. When he sings, his lips frequently don't match the words being sung.
Audio problem: When Hamlin Rule is playing the flute by the pool, he stops playing it, but the music continues even after the flute is away from his lips.
Question: It's never explained why she couldn't be Wonder Woman without doing that whirling transformation, shouldn't she still have super strength and all those abilities?
Answer: She does. However, if she were to use any of her abilities as Diana Prince, everybody, including her enemies would be able to make the connection that Diana Prince and Wonder Woman are the same person which could be used to get revenge on her. By not using her abilities in her civilian disguise, nobody would suspect anything at all and she could keep herself and her friends safe.
So it was more a choice that she decided an Ice Skating move was less conspicuous than say, ducking in a phone booth like Superman? If Clark Kent enters a a phone booth, and Superman comes out, don't you think even the dull of mind would get the connection?
That's because Clark Kent has super speed so he can easily run into a phone booth quickly and leave as Superman as quickly too or whenever Clark does need to change into Superman out in the open, there's never around to see him change. It's a plot device that's really effective.
Could one man or gal. We're supposed to just believe almost everyone these two are around can't figure out of the obvious. Characters like Spider-Man and Batman can do this because of their masks, so these excuses just don't pass with me.
Answer: As Diana Prince she didn't have the super powers that Wonder Woman has, although as an Amazon princess she does have greater strength than normal humans. Diana's mom taught her how to transform her ordinary clothes into her Wonder Woman outfit (as opposed to just doing a quick change like Clark Kent does). Her outfit, which her mother gives her when she leaves includes the "golden girdle of Gaea." The girdle provides enhanced strength and heightens her other abilities. As to why she spins, it was a stylized choice to add something extra to the show and hadn't been done in the comics. Although they did change it up a bit due to budget and time. Later, Wonder Woman comic writers would include the spin into the comics, but by then it was generally to put her into her secret identity, not to give her her powers. But as to why Diana Prince doesn't have super powers in the 70's show, as opposed to other incarnations of her; the original TV movie pilot had Diana powerless like the character was during the Bronze Age of Wonder Woman (late 60's) when Diana decided to stay on Earth and became mortal. That series was not picked up, but a 2nd attempt at it, starring Lynda Carter, was and the series loosely based Diana on the first pilot but through magic could transform into the superhero Wonder Woman.
Answer: The transformation twirling was invented for the 1970s TV series only, to explain her quick change from Diana Prince to Wonder Woman. However, it would have been nice to do a little spin homage in the movie.