We can identify beat 1 by listening to where Harry generally starts his vocal phrases. Right a the beginning he sings "Take me home, I'd love to be invited". The words "take" and "i'd" are both on beat 1. Now we have our reference. Count along while listening now if you'd like, it's fun!
The beat switch happens around 0:43 but if we listen to the solo section in general we can dissect it. He plays a repeating bass line with his left hand throughout. It is very audible from 0:50-0:53. He is doing some fancy work in the higher register but the bass line is anchoring it. There is a strong beat in this bass line. You can probably hear it naturally. It is the third note he plays in the sequence. This third note is again beat 1.
The bass line leads into beat 1 like so: "and-a-ONE". Sing along in your head. Now sing along with the bass line as he goes into his solo. You'll notice that right around 0:39 he stops playing the bass line for a moment. This is where he 'corrects' the audience. After this point the "and-a-ONE" of the bass line is no longing in unison with the clapping. If you kept your count going you'll find that it no longer matches the bass line. After he does this the clapping is now on the TWO and FOUR relative to the bass line.
Hope this helps some people. It's pretty damn cool what he did, and so smooth!
This song's meter is in 4/4, which means you count 1-2-3-4-1-2-3-4, etc. along with the very pulse you feel. Tap your foot. Count "1" when he says the word "Come [with me]". You'll find that they clap every time you say 1 and 3.
What he does is the equivalent of cutting out, say, Sunday from one week of the calendar, and so their regularly repeating clap now falls on a different day than it was falling on before. Does that help?
1 2 3 4 1 2 3 4 5 1 2 3 4 1 2 3 4
C - C - C - C - C - C - C - C - C
…so the claps (C) move from the 1 and 3 to the 2 and 4.
That fifth beat occurs at the 40-second mark, and can be spotted because he stops playing with the left hand and the right hand simply repeats what it played in the previous beat.While this might get your audience to switch over, this is trying to get your audience to skip (or add) a beat, rather than skipping or adding a beat oneself. You never actually described skipping a beat.
Stomp Stomp Clap, Stomp Stomp Clap
The "Claps" are on 2 and 4, the first stomps of the pairs are on 1 and 3. Now imagine some boob wearing his sunglasses like a hat and a popped collar starts clapping on 1 and 3: Stomp Stomp Clap, Stomp Stomp Clap
Clap Clap
That'd be annoying. The looks on Harry Connick Jr.'s face before he fixes the clapping tell it all. Stomp Stomp Clap <pause> Stomp Stomp Clap <pause>
Not: Stomp Stomp Clap Stomp Stomp ClapI could hear no difference before or after the switch -- in fact I couldn't hear any beat other than the clapping.