When Hornblower arrives for the examination, his hat is normal shape, when the officer notices him and smiles, the hat is crumbled as it was on the ship, in the previous scene.
The real HMS Indefatigable was a 38 gun heavy frigate armed with 24 pounders plus six 42 pounder carronades for a total of 44 guns, razéed from a 64 gun Ardent class ship of the line, whereas it is represented here as a 20 gun post ship.
During the examination, Captain Foster describes a situation "with Dover bearing north two miles" and a "nor'easterly wind" that "veers four points". That would put the wind at east, but Hornblower is told that he would have Dover under his lee, whereas he would, at worst, have Folkestone under his lee and that eight miles off. Unless the wind were to veer a further twelve points at gale force, the tide would never put a dismasted vessel anywhere near Dover.