As an occasional leisure sailor (who has never been near a square rigger), I have always found that in a tight situation, a good way get out of irons in a hurry is to use that nice powerful diesel engine to bring the bows round! Although I would have to add that the situation is invariably

the result of handing over the helm to another crew member!
But I think that when an admiral such as St Vincent judges the seamanship of one of his captains, he is judging his ability to get the best out of his ship, which obviously includes his ability to command others to execute his intentions. He will base his judgement on how well the ship maintains its position in the line, how promptly his signals are obeyed, whether the ship carries the right amount of sail, how well the captain keeps his ship out of danger, etc., etc.. No doubt his judgement will also be based on damage reports - sails blown out, broken spars, sprung masts, damaged bowsprits, etc.. St Vincent was a hard taskmaster; when blockading Brest he ordered that all captains must always be on deck when their ship tacked or wore, whether day or night - no doubt so that he could judge their seamanship without them trying to blame whichever lieutenant might have been in charge at the time.
Maintaining the line could be a trial, particularly at night. While blockading Cartagena, the Minotaur was constantly reducing and increasing sail, being placed 'like a pig on string' between the Prince which 'sailed like a haystack' and the Spartiate which sailed 'like a witch', the sailors declaring she was built of stolen wood, as she always sailed best at night.
It is perhaps not surprising how many collisions there were, particularly when entering and leaving port.
Regarding the Vanguard, I feel certain that Nelson would have spoken to Berry had he believed the ship to be in danger. Wounding Berry's pride would have been the last of his concerns. When Nelson wrote to his wife about the storm, he regarded the Vanguard's fate as a salutory check on his own vanity, although perhaps he was enjoying feeling magnanimous in shouldering his captain's responsibility. At a later date he actually wrote to Fanny that he did not want Berry as his flag captain because he was quite happy with Hardy, who looked after so many of the things that he would have to worry about if Berry was captain.