Local speed limit intact
Relativity forbids anything from overtaking a light beam at the same place. In a warp bubble the ship stays at rest in its own patch of space; it is the geometry around it that moves. Relative to distant observers, the bubble can still arrive before light would have.
Time machines
If a signal can travel faster than light in one reference frame, a second faster-than-light trip in another frame can bring it back before it left. Everett and Roman analysed this for Krasnikov tubes, permanent superluminal corridors: two such tubes could form a time machine. The same reasoning applies to pairs of warp bubbles.
Horizons and instability
For a bubble moving faster than light, the front wall is causally disconnected from the ship: the crew cannot send a signal to it to steer or stop. Hiscock found that quantum stress-energy diverges for superluminal bubbles in a simplified model, and Finazzi, Liberati and Barceló found that it grows exponentially at the front wall of a dynamically created bubble. McMonigal, Lewis and O’Byrne showed that particles swept up by a decelerating bubble are released with enormous energy towards the destination.