When the TARDIS is opened, the chain that opens it gets completely out of the TARDIS and falls on the ground outside. In the next shot, part of the chain is seen on the floor inside the TARDIS. On the following shot the chain is again outside.
When the Daleks exterminate Jack, the CGI skeleton's foot can clearly be seen in front of the Dalek 'sucker' when it should in fact be behind it.
Rose does not ask where Jack is or even seem to acknowledge that he is gone at the end of the episode.