Consider the physics of the American Godzilla (1998). In order to not tear itself apart every time it took a step, the Godzilla would need hyper durable muscle and bone tissue. A body composed of this kind of material would undoubtedly be extremely resistant to even heavy artillery fire. Yet somehow this Godzilla seems to be very susceptible to military weapons and survives mainly by evading the enemies attacks.
Alternately the creature doesn't have any greater pain tolerance than a regular animal, even one of its size. So while it can quite happily take hits from artillery shells and torpedoes, it doesn't particularly like to.
Since Darkman got 40% of his skin burnt off, he pretty much needs some kind of Healing Factor to avoid just dropping dead from massive infection. The third movie actually confirms that he does have one.
A deleted scene shows Hancock having sex with a female fan, and just before he climaxes he has to throw her out of the way as his super sperm shoots through the roof into space.
He hurls a Jerkass kid into the sky so high he vanishes from view, then catches the boy with a maximum of a few feet for deceleration. Really, the acceleration of how fast the child was THROWN probably should've broken his neck. Or dislocated his limbs. Or something. But at least his hair was messed up so they paid lip-service to physics, right?
An original treatment of the movie said that Hancock was able to control wind, as demonstrated in his battle with Mary when the weather gets all wonky. That would account for the lack of trauma on the kid, if the wind was slowing him to a safe speed on the way in.
He also apparently has the ability to root himself to the ground, in order to No Sell a train.
Another take on invisibility would be Hollow Man. The character Sebastian Caine gained invisibility powers that made all of his organs invisible. The problem was outlined when he screams that he can't block the strong ambient lights, since, well... if your organs are invisible, then so are your eyelids and your arms; nothing will block the light from you.
One of the more amusing scenes in Iron Man 2 is watching military scientists around the world try to kit-bash their own homemade Power Armor, but being completely unable to figure out the Required Secondary powers.
The first film features this as well. Tony initially discovers the problems of flying without stabilizers, and didn't foresee the problem with his equipment icing up at high altitudes. The "Icing problem" becomes a Chekhov's Gun near the end when it turns out that Obadiah and his team didn't consider it either.
One subplot of the second movie is that Stark himself didn't fully anticipate all the secondary tech required for the arc reactor to work perfectly either. Or at least function within a human body...
In Man of Steel, Superman has a beard at the start of the movie, but loses it by the end. The Gillette company has various well known scientists and other celebrities theorizing just how this could be possible (here's Kevin Smith's theory, for one), considering he has Nigh-Invulnerability, and therefore his body hair should be just as strong and resistant as the rest of his body. Theories range from basic applications of Material Science to grind the hair away to using the Large Hadron Collider to create mini wormholes to transport each follicle through time and space, among other wackiness.
The scene where Clark locks himself in a closet (due to sensory overload) hangs a massive lampshade on why these are needed. This becomes a plot point when he fights other Kryptonians who haven't had time to adapt.
In another scene, it doesn't matter how strong he is...Clark can't hold up part of an oil rig if the platform he's standing on bends and collapses under his feet.
Kryptonians in the film have no anchoring ability to go along with their Super Strength, so every superpowered punch sends people hurtling around like a rag doll.
In The One, all shown versions of Jet Li's character never have problems that a Super Speedster or a Lightning Bruiser should have, such as flying backwards every time he punches someone at super-speed or having his clothes ripped off by running at speeds at over 60 mph, or jumping high and leaving footprints in the road every time he moves really fast. Also, his gun doesn't seem to suffer any ill effect from being hit with a bullet from a futuristic gun, not even a scratch. Inertia also, apparently, does not exist for them, as they can go 0 to 60 in a matter of seconds and stop just as fast.
There is also the fact that Gabe seems to instinctively know how hard to hit, even though his strength and speed have been rapidly increasing for the past several months. Granted, his constant martial arts training could have something to do with this, but he seems to be genuinely surprised every time he does something superhuman.
In Stardust, Lamia puts a curse on Ditchwater Sal so that Sal will be completely unable to see, hear, feel, smell, or otherwise perceive Yvaine. The curse does give Sal one benefit: when Yvaine tries to attack Sal, she is stopped by an invisible forcefield (to ensure Sal can't feel Yvaine).
Superhero Movie lampshades this as a spoof of the superhero genre. In a brief scene, Rick Riker meets another hero who has the power to become living flame like the Fantastic Four's Human Torch, but is not immune to being burned. Thus as soon as he transforms, he immediately experiences extreme pain and begs Rick to put out the fire.
Superman Returns seems to have used this, though inconsistently, in the early "falling plane" scene. Previous incarnations would've just grabbed the plane anywhere and guided it gently to the ground. Here it rips apart repeatedly and nearly crashes despite his best efforts. Though once he got it down, he did hold the entire plane up by the nose; it scrunched the outer skin a little, but did not collapse on itself realistically.
Lifting the entire island at escape velocity, though, was pure Tactile Telekinesis.
They also show one of the downsides to Nigh-Invulnerability when, after being temporarily killed by the fall from space due to Kryptonite temporarily taking away his powers, medical staff attempt to revive Superman, only to find that his powers have returned, and the defibrillator shocks don't affect him, nor can they pierce his skin with a syringe to deliver epinephrine.
In the X-Men movies the shapeshifter Mystique is shown capable of imitating the form of another person so closely she can fool retina and voice scanners. Doing so without closely studying (practically a medical examination for the retina) the person would require some form of ESP combined with photographic memory. The novelization of X-Men 2 implies that most of the time many of her disguises are purely cosmetic, as actually replicating the textures of clothing and other materials put a strain on her abilities. As for other mutants, she is able to duplicate their appearances, voices, etc, but cannot replicate their powers, as demonstrated when she mimicked Wolverine in the first movie and her claws were cut off when he attacked her since she couldn't duplicate the adamantium in his body. True to other X-men media, Wolverine was immediately able to sniff her out as well, twice.
In X-Men Origins: Wolverine, it is shown that Fred J. Dukes has super strength and invulnerability enough to stop a tank round by punching it. However, when shown later in the film he's become morbidly obese, because he doesn't have a heightened metabolism to burn through all the pounds he's packed on due to his eating disorder. He's shown trying to work out in a boxing ring, because presumably lifting regular weights wasn't working.
Demonstrated in X-Men: Days of Future Past: Quicksilver has no problems moving at super-speeds himself (in fact, he's most comfortable that way as everything around him moves too slowly). However when he runs Magneto past a hallway full of guards during their escape from the Pentagon, Peter specifically supports Erik's head and neck to protect him from whiplash during the sudden acceleration, while afterwards Erik is visibly nauseous.
He can also hit people harder with much less force while in superspeed. He barely touches guards in superspeed, and that causes blows hard enough to render them unconscious.
The T-1000 in Terminator 2: Judgment Day is mentioned to be lacking a whole load of secondary powers. First off, it cannot assume a form that is significantly larger nor gain mass, it cannot make internal workings, only the outer surface (which is why it can't just become a bomb or a big gun, but can create swords).
A very subtle version occurs in the film I, Robot. Spooner has a robotic arm, and is seen eating a lot, including hot drinks with a ton of sugar, presumably to help power it.
Also his body is also significantly reinforced (several synthetic ribs, an artificial lung and reinforced shoulder) probably so the arm doesn't tear off should he punch at full strength. Shown as when Doctor Calvin is giving his arm a once over, her fingers slide to each rib only for Spooner to respond to her touching one with a flinch and "Hehe. Um... That one was me."
In Elysium, using an exosuit requires skeletal implants, which explains why Max can tear off a droid's head without ruining his fingers or Kruger surviving a grenade that reduces his face to a bloody mess.
Kruger's energy shield does not negate momentum, so when he's facing a high powered rifle it still knocks him back.
This is averted with the title character from Stan Lee's Lightspeed. Unlike most Speedsters, his shows actual negative effects from his power, ranging from windburn to problems with his metabolism and heart.