The maximum possible score is 282 points. A total of 247 points are earned by performing the actions required to beat the game; the remaining 35 points depend on which item (if any) you choose to take from Lily early in the game, and whether you solve any optional puzzles related to that choice.

* denotes an optional action with permanently missable points.

Actions are listed roughly in chronological order. Several actions may be performed in a different order, however.

This list is worded vaguely (a) because multiple solutions are often possible, and (b) to minimize spoilers.

To report any errors or omissions, please leave a comment. I'm afraid it won't earn you any points, but I'd appreciate it anyhow.

Unlock bedroom door (2)
Take mollusk or flask* (5)
Get rock from Artie (3)
Give Artie a drink (1)
Give Artie a second drink (1)
Give Artie a third drink (3)
Talk to creature (3)
Put first object into gumball machine (1)
Put second object into gumball machine (3)
Cut vine (8)
Convince Karg to let you cross river (4)
Cross river safely (10)
Perform first optional action related to the mollusk* (10)
Perform second optional action related to the mollusk* (20)
Reunite with Lily (5)
Get shoes from cobbler (2)
Get first signature on petition (2)
Get second signature on petition (2)
Get third signature on petition (2)
Return fully signed petition (4)
Turn dry clay into wet clay (1)
Mold clay into a shape (2)
Bake molded clay in oven (2)
Give guard captain something to replace what he lost (3)
Give guard captain something to hold the replacement in place (1)
Get guard captain to leave his post (3)
Complete deal with Hans (4)
Survive confrontation with Thurston (4)
Meet Herkimer (7)
Perform first optional action related to the flask* (10)
Use magic chain (15)
Prove your identity to Lily (2)
Get sheep to leave garden (2)
Repair Lily's dress (3)
Bribe guard (2)
Retrieve duck from fountain (2)
Prevent first competitor from interviewing (4)
Prevent second competitor from interviewing (4)
Get dress (1)
Dye dress (3)
Complete disguise (2)
Prevent third competitor from interviewing (4)
Pass interview (4)
Enter throne room (8)
Help complete story (2)
Make gumball more palatable (1)
Chew gumball (1)
Use chewed gumball on appropriate object (3)
Meet Herkimer again (5)
Unlock moneybox (2)
Combine magic string with appropriate object (1)
Wear magic string (5)
Get yourself un-stuck (2)
Use axe on appropriate object (1)
Use gold bar on appropriate object (1)
Uncork brandy (1)
Use brandy on appropriate object (1)
Activate lantern (2)
Replace missing ladder rungs (2)
Move ladder (1)
Attach chain to appropriate object (2)
Gain access to artifact box (3)
Unlock artifact box (15)
Get dungeon cell keys (1)
Escape from dungeon cell (3)
Perform second optional action related to the flask* (20)
Give magic string to Paul (1)
Give item from forest to Lily, return to forest (4)
Travel to burning forest (15)
Escape from burning forest (3)
Break free from chains (1)
Distract guards (2)
Get rope (2)
Distract king (2)
Climb onto balcony, end conflict (23)