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)
Revealing mistake: When Rose breaks Jack's handcuffs with an axe, it is obvious that she doesn't hit the handcuffs on the pipe but Jack's hand - the handcuffs come apart by themselves. The axe also bends. (02:01:30)
Continuity mistake: Look closely at the location of Rose's beauty-mark the first time you see her at the dock. It is on the opposite side of her face during the rest of the movie. (00:21:30)
Revealing mistake: When Rose is running in the hallways trying to find help for Jack when he is hand-cuffed, she finds a man and asks him to help her free Jack. She gets frustrated with him and says "listen" then hits him. In shots before you can look at the man's hand and it already has blood on it before he touches his face. This was fixed in Blu-ray version. (01:59:05)
Continuity mistake: When Jack and Fabrizio are at the bow, the anchor well below them is black. Along with that, the foremost railing is not connected with the rest. But when Rose and Jack are there the well is white and the railing connects. Plus during the "flying" sequence the gap between the vertical bits of the railing is different in different shots of the ship. (00:30:40 - 01:17:35)
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)
Continuity mistake: When the ship is about to leave the dock, there's a lot of people saying goodbye to the ones that are going to leave the city. In the following shots, you can see Jack and his friends playing cards inside the pub. If you look through the window you won't see anyone. In the next shot, when Jack leaves the pub, the crowd is there again. (00:23:15 - 00:25:05)
Continuity mistake: Right before dinner, Jack and Rose are talking to the Astors, and Molly comes up from behind them, asking Jack to escort her to dinner as well. In the next shot, when Cal calls back to Rose, Molly is still walking up to them. (00:58:15)
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)
Revealing mistake: Many scenes used computer graphics to show the length of the ship. Passengers were also added walking on deck. The shadows for the passengers don't always match. (00:30:25)
Revealing mistake: This mistake, as far as I know, can only be seen in widescreen. After Rose, Jack, Tommy and Fabrizio have run on deck (after breaking the gate down), the camera looks down the ship toward the bow. If you look at this carefully, you can see city lights in the top-left hand corner of the picture. I know these are city lights because in a book about the movie, it shows a similar picture. Fixed on Blu-ray. (02:08:05)
Continuity mistake: About half an hour in when the rear of Titanic is shown, look at the very rear of the ship and you will see a red sign (near the triple screws) to the right of an over-hanging light. Shortly afterwards when Rose approaches the rear of the ship to jump off, the sign has now moved to the other side of the light. (00:31:50 - 00:36:15)
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.