Even the game designers get it wrong sometimes.

"This always works in the movies"
The MM says that staking a vampire kills them, but there are no called shot rules and undead aren't subject to coup-de-grace. So you can't actually stake them.

"We don't need thumbs here in the Abyss"
By the MM errata, all outsiders with an Int of 6 or higher are proficient with all martial weapons. This includes Hellhounds, Howlers, and Nightmares, among other quadrapeds.

"You backwoods Dwarves still dig, what ever for?"
Wall of Iron produces real iron as an instant spell (so it can't be dispelled and is non-magical) and by the price guidelines on PHB 96 & 114 and the Avaibility guidelines on DMG 137, you can hire a wizard to cast a spell that produces roughly 1800 gp worth of iron for only 500 gp in any small town or larger settlement. And yet iron mining supposedly exists in the game world.

"Like, you know, like that.. an stuff... anat, right?"
Simulacrum produces a creature that has among other traits 51-60% of the "speech" of the original. Does that mean that it leaves random words out of ... or do it just use small words when talk?

"All the commoners round here always die off at the same time every year"
The extreme heat/extreme cold rules render much of the real world uninhabitable as everyone in Fairbanks in winter or Phoenix in summer takes enough subdual damage to render them unconscious in just a few hours.

"But I'm as strong as Heracles, made my save, and was carrying a Spade of Digging.."
Regardless of size, strength, tools on hand or reflex save result, anyone caught in the bury zone of an avalanche is pinned and must wait to be rescued rather than being able to dig their own way out.

"So that's what those pointy bits do..."
The 20th level Expert Trapmaker with Search, Profession: Trapmaker, Craft: Trapmaking, Knowledge: Famous Traps and Knowledge: Magical Traps all maxed out at 23 ranks, cannot attempt to find a trap if the Search DC is over 20, but the 1st level rogue with none of those skills can.

"I know he fled into the woods, but first, we'll check at the inn"
A Successful Wilderness lore role to Track lets you track somebody for up to 1 mile indoors, and in fact you get to retry more frequently indoors than outdoors.

Since according to PHB 121, free actions can only be performed while taking another action, and since you can only take an action on your initiative, and since by Table 8-4 on PHB 128, "Speak" is a free action: By a strict reading of the rules, you must wait until your next action to cry out in pain after being hit in combat.

"Wall of Orca"
Running away from someone? Need to block a passage? Well, have we got a solution for you! Summon Monster V allows you to summon a celestial orca. The critter has (on average) 85 hit points and it can thrash around and attack anyone trying to get through. Much better than a wall of stone. (And, since it just goes back to its home plane when it "dies," you don't really have to feel all that bad.)

"I'm not exactly feeling myself today, and neither am I"
A small spellcaster with a tiny familiar can use Polymorph Self to turn back into himself. And he can use Share Spells to have his familiar also turn back into "himself" at the same time. There aren't many spells that specifically allow you to break the normal constraints English grammar has on reflexive pronouns.

"Wow, I didn't realize dragons beer-goggled that heavily"
The various "half-" templates can be applied to any corporeal creature (alignment permitting). This includes oozes, plants and even constructs.

"I never Meta-magic I didn't like."
Silent Power Word, Kill.
Still Burning Hands.

"Transmute Rock to Stone"
Type elemental provides immunity only to poisons, sleep, paralysis, stunning and critical hits. So it is still possible for a Gorgon, Medusa, Cockatrice or Basilisk to petrify an Earth Elemental.

"Trees; you can chop 'em down, but you can't change 'em with magic"
As per MM 6, plants are immune to polymorphing. Presumably this includes Polymorph any Object, even though the spell description uses "vegetable" as a classifier.

"So much dropping a GP off the Empire State building"
An arrow fired from a bow or flung via Telekinesis deals 1d6 or more damage, yet the same arrow dropped from a great height can never deal any damage, since it weighs less than one pound (DMG 89, column 2)

"I command you to fall down and crush my enemies"
Conversely, a Greater Earth Elemental that falls 10' does 270d6 points of crushing damage to everything under it (conceivably a 35' x 10' area). Since the first ten feet of a drop is subdual damage, to which elementals are immune, they can make this ten-foot drop without so much as a scratch .

"Azathoth's Gibbering Explained??"
Deities are capable of casting Contact Other Plane to converse with themselves - but they "resent such intrusion" and even have a flat percentage chance of lying to themselves.

"Mad cat!"
A house cat, accoring to the MM, can deal 3 damage with two claws and a bite. (Minimum damage is 1 HP for an attack.) And a peasant has 1d4 HP. So don't tick off kitty!

"It's Big, It's Heavy, It's Wood!"
Since a club costs 0 gp, a Limited Wish spell can create an infinite number of clubs, causing the plane to collapse into a black hole.

"Why yes, I did bring weapons for the entire army"
Since the sling has both cost 0 and weight 0, and you can generally find ordinary stones for free, there is no mechanical reason not to carry a few million around in case you need to arm a peasant uprising.

"Dagger, Greatclub it's about the same"
The MM errata failed to amend the Tarrasque's Swallow Whole ability to mention the usual stipulation that you can only cut your way out with a "light slashing or piercing weapon".

"If the horses ever catch on, we're in trouble"
A whip cannot even deal subdual damage to any creature with a +3 or better natural armor bonus. This includes all horses, which makes you wonder about coachmen and the use of riding crops.

"It's all in the trunk"
Dire Elephants, as described in MotW, have a +23 skill bonus to Climb, and are listed as having speed 40 ft., Climb 10.

"It's Not So Good Up Close When They're Standing Still"
Although it ignores armor (as it normally requires only a ranged touch attack to hit), and is specifically noted as creating a "magical arrow", Melf's Acid Arrow cannot be used to perform a Coup de Grace against an adjacent foe in the manner a normal bow can (PHB 133). For that matter, neither can a sling, although a hand crossbow works just fine.

"Never trust a used weapon salesman"
Despite the really cool part about the ability not allowing a saving throw, that's just clever advertising intended to distract you from the fact that the complete destruction effect of a Mace of Smiting only functions when you deal a critical hit to a construct - which are not subject to the effects of critical hits.

And watch out for those vorpal weapons too, they have to be fabricated using a spell that doesn't exist in 3rd edition.

"Butter-fingered Balors"
Balor's vorpal sword is only a +1 weapon... This means that it's almost entirely useless vs most other demons and devils. Why don't they simply get a +5 keen or defending weapon? Is that so that they don't accidently cut themselves?

"He's just faking it..."
Despite being blind, Grimlocks have a Spot check of +3.

"Class-ical Blunders"
Apprentice-level paladins have lay on hands as a class ability, but have an effective level of 0.

Wizards, druids, and monks do not have Unarmed Strike as a weapon proficiency and the druid loses all abilities for 24 hours if she tries to punch someone, or if she Wild Shapes into an animal and bites them.

A Cleric with the Water Domain can turn Fire Creatures like a normal cleric turns Undead. So Clerics with the Water Domain can turn Red Dragons. In fact, the only dragons that cannot be turned are white, the weakest of all colors.

"Forget stone, build my castle out of dwarves!"
The disintegrate spell cast on an object will destroy 10 cubic feet of matter, no saving throw allowed. The same spell will only affect one dwarf, who the caster must hit first with a touch attack roll, and still gets a saving throw.

"In the eye of the beholder"
Hill Giants are described as "oddly simian", who "seldom wash" and carry "filthy, and stinky" possesions. Cloud Giants are "handsome" and "well-defined" who wear "the finest clothing available." Hill Giants have a charisma of 17; Cloud Giants have a 13.

Thanks to Talen for the original "3ed Humour" list. Used with permission.