Continuity mistake: After Alice is knocked over by the paperboy she goes inside where Carol is pouring sugar in her coffee. Watch the amount of sugar in the container increase when the camera angle changes.
Continuity mistake: When the electric wire falls on the ground, it's torn but when Cindy comes to take her ball, it's almost completely straight.
Continuity mistake: When Mr. Dittmeyer is sitting on the toilet, just before the floor collapses, when seen from his point of view, there is a lot of debris and other objects around the base of the toilet. From the wide shot, when the floor collapses, most of the objects are gone.
Factual error: Sam prepares twenty lbs. of meat for Carol but when he gives her the package, it is way too small to be twenty lbs of meat. Ten lbs at most.
Continuity mistake: When Marcia opens her drawer to see if Jan has taken her socks, she opens it with her left hand. In the close-up, she's using her right arm.
Visible crew/equipment: The camera car, which is followed by a motorcycle cop in a white helmet, is visibly reflected in a couple of store windows, in the first minute of the movie. (00:00:25)
Continuity mistake: When you look at the house from the outside the upstairs is on the left. But, when you go inside facing the same direction, the upstairs is on the right.
Continuity mistake: When Gregg play guitar and Cindy enters the chamber, his strap keeps changing over and under his collar.
Audio problem: When Jan hits Mr. Dittmeyer with her bike, she drives off with the cord and handset attached to the pedal, however we hear someone saying "hello" which would have not been possible given it was no longer connected to the base.
Continuity mistake: When the family comes back home after Jan ran away, she has 2 rollers on the sides of her head. Throughout the scene, the height of the one on the right varies from high up near her hairline to midway down just above her eyebrow.
Deliberate mistake: In the Search for the Stars contest, at the end of the song their mouths have stopped singing as they go to bow but you continue to keep hearing them apparently sing a few seconds longer as it fades out. This is a joke referring to the original Brady Bunch episode where the kids sing the song on live television and the song similarly fades out after they've stopped singing.
Continuity mistake: During the scene in which Marsha is going on a date after her football injury, the amount her nose is swollen and bruising varies between noticeable to almost non-existent throughout all the scenes that occur the night of the dance. (00:44:15 - 00:45:15)
Plot hole: Even though the Brady Bunch kids won $20,000 (check, not cash) in the "Search for the Stars" contest, they would not have immediate access to it, so would not be able to merely take the oversized representative check - which would be nonlegal tender - to pay for the taxes; they would have to wait until they received an authentic hard copy (real check) and wait until the check "cleared" the bank (was legitimate and payable). Clearing the check could take weeks because the Brady's didn't have at least $20,000 in their checking account to cover what could be a bogus check. (01:19:03)
Continuity mistake: When Alice hands Greg the newspaper and says "dont bend over", he begins to unfold it in the close up but when it cuts to the far away shot, he is beginning to unfold it again.
Revealing mistake: When the family heads to Sears and are first playing with the cameras, Jan's show that her movements in her camera are slightly different and not the lag factor of the image being displayed on the TV.
Revealing mistake: During the scene where Mr. Dittmeyer is standing in front of the 9 TVs, you can see that the middle 3 people (Mike, Carol and Alice) are all taken from the same camera/angle as they all have the same background. As such that would then mean they were recordings being played back vs. being live shots as beginning of the musical number portrays.
Answer: I have listened several times to both versions of "Sunshine Day" on YouTube. To my ear, they are both the same speed. However, the movie version does have some significant cuts, and some added incidental bridge music, such as when the crowd of women rushes to the Tori Spelling book signing, or when the kids are talking to Alice in the massage chair. If the movie version is slower, it is not significantly so. And perhaps it was changed to fit the blocked movement they wanted, and to accommodate the timing of the scene that they were going for. I doubt legality had anything to do with it, as the soundtrack notes states the song was used by permission. But, again, I don't think the tempo has been significantly altered.
The original series was faster. I just listened to the start of both versions a few times in a row and although they are both in the same exact key (key of A), the show is definitely faster tempo and the movie slower. Even the singer in the first line of the song (one of the girls) sounds higher pitched in the show, and slower and lower pitched in the movie.