You can review the surveillance videos once you have the timecard from the museum guard. You can find him at the Clown Store.
You go into the Surveillance room Via the security room or the tunnel in the museum tour (near the mimes).
There are no snowballs on Counterfeit Island. (see the related question)
Go into the bottom right room and see all the videos. Then mews will show up.
The inspector is not around to see the "dragon picture", because you get the last piece in the Supply Room. She does see the "thief" picture when you print it from the video surveillance tapes. But she says she doesn't recognize him.
There does not seem to be any lava anywhere on Counterfeit Island. (see related question)
The security guard who was on duty is in the Clown Store. Get his timecard to find out when the theft occurred, and you can see it on the surveillance video. (As it turns out, it was about 4 AM, but knowing that will not help without the timecard.)
(see the related questions)
When the painting is stolen, get the timecard from the night security guard (he's in the Clown Store). Then you can see the theft on the videos in the Security Room of the museum.
you can't
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Go to the Clown store and get the time card from the museum guard. with that, you can narrow the time to see the theft on the museum's Security Room videos. Get a photo of the thief (it's the shady guy) and show it Downtown.