In "Blink," Sally Sparrow had many pictures of the Weeping Angels in her folder she gave the Doctor later. Here, the Angel on the tape comes to life because "that which captures the image of an Angel becomes an Angel," so the pictures Sally gave the Doctor in "Blink" should have come to life.
When the Doctor is with River and Amy, discussing the Weeping Angels' defense mechanism inside the pod with the looping video screen, he holds onto what appears to be a safety harness dangling from the ceiling. This immediately tears off, and he throws it somewhere out of the way. However, Matt Smith initially did this accidentally, but they decided they liked it and even re-filmed it.
When the TARDIS materializes to catch River Song, the earlier Davies-era model is used by mistake. It can be distinguished by the missing St John's Ambulance logo, the lack of white window frames and the slightly different color scheme.
When Amy is yelling, "Does anyone need me?" the door behind her says "Caution, Trip Hazzard." "Hazard" is spelled wrong.
When the Doctor and Amy explore the museum's nave and its artifacts, the TARDIS is nowhere visible on the nave. (Both nave perspectives have been displayed). A few seconds later, when they are escaping to the TARDIS, this one is parked in plain sight in the middle of this very same nave, near one extremity.
The story is set in the 51st century yet the clerics' weapons & uniforms are basically the same as today. In the intervening 3000 years one would think that the guns would fire lasers rather than bullets, which would destroy the angels, especially since the spitfires had lasers in the previous episode.