Visible crew/equipment: When Jack comes to the first class door for the first time in his tux, you can see a cameraman in the glass door just before he enters. (00:54:55)
Visible crew/equipment: When Jack and Rose are running away from Cal to the first class dining room, if you look at the glass you can see a black screen, a light, and a crewman. Fixed in the Blu-ray version. (02:20:32)
Visible crew/equipment: As Jack is getting ready to draw, when Rose comes out you can see a hand opening the door for her. (01:21:40)
Visible crew/equipment: When the captain goes to the wheelhouse, which is flooding, you can see the shadow of a camera at the bottom left corner. (02:22:10)
Visible crew/equipment: When Rose says her line "Yes, I would like to see my drawing" when she is in her stateroom with Lizzie, the shadow of what appears to be a boom mike (behind her and to the left) can be seen dropping down prior to her line and then going back up afterward. (00:15:00)
Visible crew/equipment: When handcuffed Jack tells Rose he's glad she found he wasn't a thief, a boom mike is reflected on the porthole's glass. In wider shots it disappears. (01:55:40)
Visible crew/equipment: When Jack and Rose are running away from Lovejoy (Cal's servant/friend), they run round a corner on E-deck. When the camera follows, the camera's shadow can be seen on the wall. (01:28:45)
Visible crew/equipment: When Jack and Rose are running from Lovejoy, they stop for a moment on E deck. When they do, look behind them and a member of the ship's crew comes into shot holding a bag of something. When Jack and Rose start running again, this man has disappeared. (01:28:20)
Visible crew/equipment: When Jack and Rose enter the car to make love, cameras, shades, boom mic and studio structure are reflected on the brass parts of the car. (01:29:30)
Visible crew/equipment: In the scene after Jack and Rose try to save the child from the Italian guy, when the water bursts through the doors, they run away from it. But take a close look at Jack's neck: you can see the edge of a black wetsuit. And under his entire shirt, it's a little darker than it is a few moments later when they try to open the gate. (02:16:45)
Visible crew/equipment: When old Rose is traveling in the helicopter at the beginning of the movie, the skids of the filming helicopter can be seen reflected in the window of the one Rose is in. (00:13:02)
Visible crew/equipment: When we see Jack moving the sofa for Rose to lie on, look in the window behind him to the right. You can see the cameraman's shadow moving with the camera. (01:21:25)
Chosen answer: During the several years it took to construct the ship probably, or in any of the supplies/food brought on board, or in the furniture brought on board. A single pregnant female rat can be responsible for thousands of rats in a very short space of time (the offspring are not too choosy about who they breed with).
Soylent Purple
A pregnant female rat could have made a home in a underneath a third class couch and had the other rats then all the females would have baby rats quickly.