In the scene where Roger and Anita are in the park, Roger puts his hat down on the bench. Later, when the dogs get both of them into the pond, Roger comes out of the water with his dripping hat on his head. I've seen this movie multiple times, and I have never been able to convince myself that this is anything but a slip-up.
No, I just watched the movie this weekend. Pongo takes the hat, and sets it on the bench. Roger leaps and lands on Pongo's back. The next thing we see is Roger hooking the leash onto Pongo's collar and then Pongo takes off and in the next scene you see Roger tip his hat to Anita after Pongo has wound the leash around their legs. No where in this series events does Roger pick up his hat.
I just watched the scene several times. It is definitely a goof up, but Roger actually has his hat before they end up in the pond. The only way that Disney can explain this is to say that Roger (being a very tall, lanky individual) reached back toward the bench and grabbed his hat while being pulled away by the leashed dog. I'm watching the Full Screen version though, so I'm not 100% sure if Roger is actually out of the shot. He is out of the shot on the Full Screen version, but that explanation is still a bit of a reach (pun fully intended).