Abandon Ship: Numerous men are shown bailing out of their crippled fighters and bombers through the film. Just as many are shown desperately trying to do so and failing, including one very long drawn out wide shot of a British fighter diving out of the sky trailing smoke, the pilot struggling to open his canopy, before we see the distant explosion as it hits the ground.
Ace Pilot: To be expected in a film about aerial warfare; both sides have some of these. Colin Harvey and "Skipper" fit the stereotype best (in terms of looks and manner), but any named character with pilot's wings who isn't dead by the end of the film is at least an honourary example.
America Saves the Day: Averted, as the entire film takes place before America's entry into the film. That said, the (neutral) Americans spend the entire film just Out of Focus, with the Brits trying to wrangle various support from them while the Germans try to convince them that Britain is on the ropes.
Battle Couple: Deconstructed. In fact, quite possibly an Unbuilt Trope in this film: Colin is entirely opposed to Maggie serving in uniform at all, as he'd rather she stay at home where it's safe. Maggie meanwhile feels driven by duty and tries to get her husband to understand why she insists. The war is a source of constant stress and fuel for conflict in their marriage.
Blatant Lies: A radio announcement stating that 'several RAF Aerodromes were also attacked, and some casualties were sustained, but they were light'... playing over a shot of the smouldering ruins of one of said aerodromes.
The Cavalry: Inverted and Averted early in the film. Air Chief Marshal Dowding's introduction is a monologue explaining why the RAF cannot afford to help the French any further.
Cool Plane: Quite a few, actually, both British and German.
Crowd Panic: When the lights go out in Berlin and the air raid sirens begin to sound, the civilians immediately start fleeing to find shelter.
Eagle Squadron: Most notably, the Polish, Czech and Canadian pilots fighting for the Royal Air Force, but the credits include a list of different nations whose pilots fought for Britain during the titular battle.
As a point of trivia, the Trope Namer, the three Eagle Squadrons of American volunteers that served in the RAF, do not appear in this film because those squadrons did not become operational until after the battle.
Everyone Calls Him Barkeep: Robert Shaw's character is known to the audience only as "Skipper" (his men's nickname for him) and "Rabbit Leader" (his callsign).
Fighter Launching Sequence: Obviously. Air Vice Marshal Park frequently complains that the fighters don't take off quickly enough to stop the German bombers before they reach their targets.
Skipper: (As their airfield is under German air attack) Well don't just stand there! Get one up!
Foreshadowing: Harvey meets an RAF officer who had been burned badly and is visibly put off by it. Her husband ends up caught in a burning Spitfire in the next battle sequence. He escapes, but is badly burned.
Home Guard: Of the Torches and Pitchforks variety, showing how desparate Britain's situation is during this campaign. Also, after their radar stations are hit, the RAF is left to rely on the Observer Corps to spot the bombers visually and report in.
Hypocritical Humor: Group Captain Baker is in the middle of lecturing Maggie Harvey about how the practice of male and female personnel sharing the same trenches during air raid drills has got to stop. He is interrupted by the onset of a German raid on their base, and he and Maggie both dive into the nearest trench.
Maggie Harvey herself has a bit of this after a raid herself. She shakily pulls out a cigarette and is shouted at by a male officer because she could easily ignite a fuel leak with a lit cigarette. In response, she briefly loses her Stiff Upper Lip.
Don't you yell at me, Mr. Warrick!
Just Plane Wrong: There are a number of inaccuracies in that department, although they made quite an effort to avoid this as far as possible. One particularly notable instance is in sequences with groups of Hurricanes on approach Bf 109s stand in for more Hurricanes in the background, leading to the entertaining fact that they're basically heading into battle with enemies on their tail.
There is another little fun bit of this, although very slight - The Spanish HA-1112s and CASA 2.111s (license-built versions of the Bf-109 and He-111 respectively) used for the film were powered by Rolls Royce Merlin engines and easily distinguishable from their German counterparts by the bulky air-intake under the engine. So the vast majority of planes in the movie - on both sides - used the same engine.
Crash scenes and unavailable aircraft (such as the Ju-87 Stuka of which no flying examples exist) were done using large-scale radio-controlled models.
Language Barrier: 303 Squadron is manned by Polish expatriates. They are very enthusiastic, but are unable to communicate effectively with their English comrades. After being mistaken for a German and taken prisoner, Hogs can be seen studying a Polish-English Dictionary late in the film.
Men Are the Expendable Gender: Averted. Bombers do not distinguish between gender, and a number of WRAF ground personnel are killed in raids on British bases. Not to mention the civilians, including women and children, when London is bombed.
New Meat: Several replacement pilots. Most get killed off fairly quickly (one on his first sortie) Only one lives long enough to become a Shell-Shocked Senior, he and one of two newbies who arrived just before the last big battle sequence are the only ones who survive the whole film.
Seemingly played straight by Colin Harvey, who doesn't sound British at all... but if you look at his uniform carefully, it is revealed that he's actually Canadian. This is never brought up in dialogue.
Canadian Christopher Plummer insisted on having the "Canada" flash on his uniform.
Not So Different: British and German forces alike are shown to partake in good-natured joking around and sharing of advice between missions.
Present Day Past: One map shows London with its post-1967 boundaries, much bigger than it was during the war. Probably an oversight by the props department.
Red Alert: If Dispersal calmly puts the phone back on the hook, Averted. If he slams the phone and runs to the window...
Sitting Duck: Throughout the early part of the movie, many British planes fail to get off the ground before being shot up by the Luftwaffe.
Indeed, an early scene has an airfield in France in the midst of being abandoned. The planes that aren't able to fly out on their own are doused in gasoline so the Brits can destroy them and keep them out of German hands. The Germans just happen to show up on cue to shoot up the now highly-flammable planes.
Stiff Upper Lip: The British (obviously), but the German pilots display this as well.
Stuff Blowing Up: Both sides' aeroplanes tend to explode spectacularly when hit. This is because a) real airplanes are full of gasoline and b) given the special effects techniques available at the time the only practical way to show a real airplane being destroyed in flight was to matte an explosion over it in post production. The model shots avoid this, naturally.
Tempting Fate "You know what our friend Goering said: "If ever a bomb falls on Berlin, you may call me 'Meier.'"
Translation Convention: One of the first World War II films to avert this. The British, French, Germans and even the Poles speak their own language. The latter is actually a Plot Point, as problems created by the language barrier between Polish volunteers and their RAF commanders were fully Truth in Television. Non-English dialogue is not subtitled whenever the context makes it unnecessary.
It also comes up when a Polish pilot is shot down, bails out and lands in a field - where the farmers mistake him for a German pilot because of his accent.
In the scene where they parachute into the church, one of the women asks (in French) if they are Angels, which is not subtitled at all, but is very emotional if you understood what she said.
Unreliable Narrator: The BBC broadcasts heard throughout the film, occasionally giving a somewhat... softer reporting of the events that we have just seen.
Vomit Discretion Shot: At the end of the film, Dispersal's phone rings (which throughout the film has had a 50/50 chance of meaning a Scramble). Turns out that this time it just means the tea is ready. One Ensign Newbie is polite enough to step outside before leaning over to nervously puke.
War Is Hell: German and British pilots alike meet very unpleasant ends. One of the main characters is last seen trying ot bail out of a plane whlie his cockpit is engulfed in flames. We are told later that he bailed out and survived, but suffered severe burns over most of his body. The aftermath of one air raid includes a row of dead Women's Auxiliary Air Force personnel covered by a tarp. Another scene shows that a church hall full of civilians (including the family of one of the main characters) shown in a previous scene has suffered a direct hit. By the end of the film, German and British pilots alike are shown to be badly strung out, the British units full of nervous newbies (most of the experienced pilots having been shot down by now) and the German units shown to be badly thinned by attrition (not receiving replacements as quickly as the Britons are).
We Used to Be Friends: The British and German ambassadors in Switzerland. Judging by how the British ambassador's wife greets the German ambassador, it's clear that they used to be on much better terms before the war.