Deliberate mistake: During the 6/11/04 episode, Jax and Courtney are having dinner in Italy. Carly, who is in New York, does some sleuthing, finds out where Jax and Courtney are, and flies to Italy. Miraculously, Carly manges to fly from New York to Italy and arrive while Jax and Courtney are still eating dinner.
Battlefield - S26-E1
Deliberate mistake: Look for the "creases" in the wall inside the TARDIS, which look as if the wall was just a sheet hung up behind the console. (In fact it actually WAS a sheet and not a "solid" wall - the TARDIS wall prop was apparently unusable due to water damage, due to poor storage between seasons. This also explains the lack of TARDIS interior scenes throughout the rest of season 26: it was not thought worth repairing the TARDIS set [or building a new one] when the show was in imminent danger of being cancelled after season 26).
Deliberate mistake: Amanda survives a plane crash into the ocean, hurricane winds in a life raft, then experimentation and attacks by giant microbes inside the alien probe. Yet when she and the others are rescued at the end, not one strand of hair is loose in her 1960s "beehive" hairdo. (00:49:05)