LemonLord7 and Ripper62 from Reddit compiled these a large set of clarifications to and lesser-known rules. I thought I'd organise the list, find the sources and tidy up the answers a little. Hopefully you'll find it a useful resource for next time there's an debate.

Spells

Many spells can only target creatures and not objects - check what they can act on. Also, objects are immune to poison and psychic damage, but otherwise they can be affected by physical and magical attacks much like creatures - PHB p185, Interacting with Objects

Readying a spell requires concentration until the casting or the beginning the next turn, and expends the spell slot whether or not it casts - PHB p193, Ready

Roll once only for spells affecting multiple creatures. The rolled damage is applied to every target - PHB p196, Damage Rolls

Casting a spell as a bonus action means you can only cast cantrips for the rest of your turn - PHB p202, Bonus Action. Note it's a bonus action, and not casting two spells. If you have Action Surge, then you can cast two spells in one turn, since no bonus action is used to do so

Not all spellcasters can cast spells as rituals - PHB p201-202, Rituals

Charmed targets can't attack the charmer or target them with harmful abilities or spells - PHB p290, Charmed

Attacks

When an Attack of Opportunity happens on someone else's turn, a rogue's Sneak damage can be applied, but a fighter's Extra Attack cannot. The same applies to readied actions. PHB p96, Sneak Attack (Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack)

Action Surge does not give a bonus action; it's just poorly worded. A better wording would be "On your turn, on top of your regular action (and possible bonus action), you can take one additional action. PHB p172, Action Surge

A round is one turn from every combatant. A turn is when one combatant/group of combatants acts in the round. PHB p189, The Order of Combat

Attacks of Opportunity happen prior to a creature moving out of your reach, Readied Actions happen after a trigger. PHB p195, Opportunity Attacks & PHB p193, Ready

Half cover gives a +2 to both AC & DEX saves. 3/4 cover increases this to +5, unless attacker has the Sharpshooter or Spell Sniper feats. PHB p196, Cover

Attacks with nets are always made with disadvantage, unless fighting underwater. This link & PBH p198, Underwater Combat

Combat

All enemy NPCs of the same type have the same initiative. PHB p189, Initiative

If an opponent is within melee range, you suffer disadvantage when making any ranged attack, not just targeting the melee-opponent. This doesn't apply if the enemy is incapacitated. PHB p195, Ranged Attacks in Close Combat

ranged attack, not just targeting the melee-opponent. This doesn't apply if the enemy is incapacitated. PHB p195, Ranged Attacks in Close Combat Resistance and then vulnerability are applied after all other modifiers to damage. Also, round different types of damage individually; e.g., if you are hit with Flame Tongue and suffer 9 slashing and 7 fire damage, and you have Resistance to both, you round down each separately. PHB p197, Vulnerability

You can take your reaction on your turn; e.g., counterspelling Counterspell - see this Sage Advice column Extra Attack only grants additional attacks when you take the attack action on your turn. If you ready an action to attack, you can only make 1 attack, unless your trigger occurs before you end your turn. PHB p49, Extra Attack

Feats

Since Jack of All Trades works with all ability checks, and in 5e all checks are ability checks, this includes initiative rolls and spells like Counterspell. PHB p54, Jack of All Trades & p174, Ability Checks

Rests

You can only have 1 long rest per 24 hours. Taking a second long rest just means you're rested. Also, a long rest can be interrupted by up to an hour of activities (combat, casting spells, travelling etc), or 2 hours of light activity (talking, eating etc) and still give the benefits it should. PHB p186, Long Rest

Advantage & Disadvantage

Causes don't stack - you either have it or your don't, and having both means you get neither, irrespective of how many of each you have. PHB p173, Advantage and Disadvantage

Darkness/fog provide cancel out advantage and disadvantage if both targets can't see each other (you can't aim, they can't see it coming) due to using the rules for Blindness. PHB p183, Vision and Light & PHB p290, Blinded

Each gives +/-5 respectively to passive checks. These bonuses do not stack. PHB p175, Passive Checks

Frightened imposes disadvantage on all attacks and ability checks. The sufferer can't move closer to source of fear, whilst they have Line of Sight to it. PHB p290, Frightened

Resources

Harvesting poison from a creature is a DC20 Intelligence (Nature) check. DMG p258, Crafting and Harvesting Poison

Component pouches aren't standard equipment. Buy one if you'll need it

Other