A Serpent stops you entering its cave?
A bit of digging is called for. Use the helmet - a few times.
Cover your eyes with the Cloak to pass the Serpent.
Keep dying when you try to cross the Chasm wearing the Armour?
Some sort of primitive bridge might help.
Kill the Mastadon with the dagger and use the Branch to cross.
Can't get the Icicle?
Singing  won't help - be a little more drastic.
Hit the Icicle with the Boulder.
Can't kill the Bear?
You could if it couldn't see you.
Throw the Cloak over it and kill it with the Icicle.
Trouble with the Cavemen hunters?
Some protection is needed here - and paint an eye on your face.
Wear the Armour, Skullcap, Necklace, carry Bear's skin.
Can't get past the Wolves?
They're hungry.
Give them the meat from the dead Bear.
Can't kill the Rat?
Slow it down a bit.
Give it the bread, then kill it with the Flint.
The sentry won't let you into the Caverns?
Patience and perhaps, a gift?
Wait until the Ceremony is over then give the Sentry the Wine.
Priest won't let you have a Candle?
He might if you showed a little respect.
Pray at the Altar.
Can't get out of the Inn kitchen with the Pot and the Cleaver?
Maybe if you lost your temper?
Hit the door with the Pot.
You could use a rope, but the Priest is being unhelpful?
Find a way to dull his hearing.
Put some Wax in his ears.
Is there another exit from the Church Vault?
The Sconces might prove helpful.
Turn Sconce 8 clockwise.
Is there another exit from the Bottom of the Well?
A spot of digging might tell you.
Dig in the Mud with the Cooking Pot.
Trouble with a collapsing roof?
Better shore it up.
Put the Barrel in the Chute and chop the Barrel with the Cleaver.
Can't get on to the Beach?
Do a spot of time-travelling.
Leave everything you've collected, then use the Time Capsule.
A soldier is blocking your way?
Try the banana-skin type of solution.
Empty the bottle of oil and attack him when he slips.
Problems with the Rat?
Watch out for its bite and block its escape route.
Carry the hypodermic in case it bites you; drop Net in tunnel.
Stinging insects stopping you from getting some red Berries?
Find them something else to eat, rather than you.
Get the dead fish from the sea and drop it beside them.
Can't catch the Pig?
First you need to follow it. Try a spot of hedge cutting.
Cut foliage with axe to find pool, poison pool with berries.
The Bats giving you trouble? 
You can't kill them, so try to disperse them with smoke.
Burn the dead Leaves and the Guano in the cave.
Being eaten by Sharks?
Oink! Oink!
Feed the dead Pig to them.
Can't cross the Lava flames?
Timing is everything.
Carry Watch, examine Flames, Time Flames and Jump Chasm.
What to do with the Treasure Chest?
Maybe you could swap it for something useful.
The Ship's Captain offers a Harpoon Gun for it - accept it.
How to get to the top of the Volcano?
Do a spot of climbing, but you'll need a little help.
Fire the Harpoon Gun under the branch.
Fumes at the lip of the Volcano causing you problems?
Pity you don't have a Gas Mask!
Just hold your breath.