So to start, your scene in the Harry Potter Film did in all likelyhood not play out that way in the book (To be perfectly fair, I've never watched "The Order of the Pheonix" because the book was my favorite of the series (the book came out the summer after a nightmare school year for me due in large part to a new incompetent and community meddling teacher of one of my favoirite subjects and one of my favorite subdisciplines of that subject to boot. Umbridge was so close to home for me, that it was rather fun watching a similar teacher get her comeupance. That said, the real teacher was no where near as nasty as mine... though both did hate Harry Potter) and all films up to that point failed to meet my expectations thus far, I opt to not see it to preserve my fond memories of one of my favorite books of all time.)
In the scene in question (I think, there are two scenes where the characters confront but I'm pretty sure the scene in question was not the first classroom observation) Umbridge and McGonagall were seated (the height dominance was always in McGonagall's favor as she was fairly tall woman, while Umbridge was described as being so short that there was no noticable difference in her standing height vs. seated on a chair height... the fact that Umbridge was this short is the only mention of height in the scene if mentioned at all). Rather, the tension is built through the dialog which was subtle and striking in insults traded. Umbridge here loses, because her constant corrections of political corrections of all of McGonagall's statements, while McGonagall's cuts to Umbridge are brutal both from a professional and personal standpoint. In this scene the two character's exchange that both women hate each other and while Umbridge is trying to remain diplomatic in her corrections of McGonagall's trival and forgivable flaws, McGonagall is the first to directly attack, but not out of losing her cool, but recognizing the passive aggressive nature of Umbridge and proceeding to drop the pretense and get to what they both knew was going to happen.
Perhaps the most devastating blow comes when McGonagall points out that Harry needs perfect marks in his Defense Against the Dark Arts classes (which she is teaching), which McGonagall responds that he has recieved perfect marks. When she points out his grades are slipping in her class, McGonagall snaps back that she really meant all his DoADA classes taught by a COMPETENT teacher. This line has been disected repeatedly in the fandom, but not only is McGonagall straight up saying she doesn't think Umbridge deserves to be called a Professor at Hogwarts, but that of the 5 DoADA teachers Harry has had up to this point, Umbridge is the worst in a motly assortment of one term teachers who include a man who was afraid of his own shadow and had the villain of the series stuck to the back of his head the whole time, a self-absorbed con-man who suffered magical induced amnesia after messing up the one type of magic he was acctually pretty decent at, a werewolf who was on brink of homelessness before taking the job, and a wolf in sheeps clothing madman pretender who's idea of teaching DoADA was using the Dark Arts on his own students (which would be tandem to teaching Electrical Engineering students by giving them periodic shock thearapy until they figured it out). Out of this, only one could have been truly agreed to have been competent (the Werewolf) and while it's not a dig from the reader's knowledge of the teachers personal flaws, Umbridge is a very openly bigoted person and believes Werewolves to be second class citizens, which is why the poor fellow was near homeless at that point in time. The insult hurts both professionally, as only one of the teachers would objectively qualify as competent (The werewolf) while its debateable at best with two (The timid one and the Madman Pretender) and objectively true with the Con-Artist. But of all of them, the by the books obstructive beuracrat was the only one who meets McGonagall's very low bar for incomptence in teaching.
Again, it took a long break down to explain why the insult was so effective that it decisively ended the battle... the actual line is... a single line. It's powerful for it's effective shut down of Umbridge's petty quibbles with McGonagall's politically incorrect teaching style, yet subtle in that so much is understood in the implications that isn't said. Umbridge already showed the readers she looks down on the past four occupants of her current role, so she, along with readers who are five books in, are well aware of the slate of contenders for worst teacher of this class to this point. And McGonagall is well known to be second only to Dumbledoore in skill as a teacher, thus lending weight to the blow.
But you can look to the same book to see subtle symbolic things in the background. While cleaning #12 Grimauld place in the beginning of the book, the narration goes through several cleaning chores that the group undertakes to make the place livable after a decade of abandonment and preceeded by the occupation of a very old family of mostly Dark Wizards and their collection of dark artifacts. Among the list of many ominious objects and unuaual behaviors that made them creepy, only one, which seemed broken, was given a few lines before being discarded. It wasn't until the very end of the next book that we learn it's the least notable object of the set that actually was vitally important to the entire storyline that had been building (fans were able to put it together from what was thought to be a subtle clue by Rowling, though this is less a failing on her part and more due to the fact that after 6 books of her writing, fans had come to know that Rowling will slip important details into the story well before they actually become plot relevant... They were expecting the clue to already tie to establised teritary characters and plot points in the series grand lore.).
Edit: There should also be note that in Literature, small sutle background events that become important later are called Chekov's Guns (I.E. The mysterious Locket). Symbolism are items or details that signal a character or ideological topic repeatedly used in the story (Hogwarts House Colors and Animals, A lighnting bolt scar) and in audio-visual works, a musical piece that symbolizes a character is called a lietmotiff and will play whenever the character is on screen or something important to the character occurs (The opening music score in all Harry Potter films is called "Hedwigs Theme" and plays anytime she or Harry are on screen. In Star Wars, "The Imperial March" plays whenever the Empire, or especially Darth Vader are on screen in the original trilogy and whenever a step towards the Empire's rise or Anikan's fall occurs in the prequel trilogy.). A piece of dialog that carries a greater amount of information than what is actually verbally said by the character is called subtext. A line that hints at a future event in the story is called "Forshadow" while in a prequel, a line that references an already known to the audience event is often a "Call forward" and may also be an example of Irony (In Smallville, which is about Clark Kent's teenage years before he became the man who will be Superman, a character saying "Clark Kent represents Truth, Justice, and the American Way" would be a Call Forward and a Forshadow if the audicene didn't know a lick about Superman. Another line where Clark sees an ancient greek armor set with a prominent S emblazoned on it's chest and remarks "I wouldn't be caught dead wearing that into battle" is Irony as the audience is aware that he most certainly will.).
All of these have symbolic importance but not necessarily for the same reason.