Credit to MorteIncarnatum over at TrueAchievements for this list of missable weapons and costume items:
FIRST VISIT TO SCHOOL:
Dodgeball — [Missable] During your first visit to the school you will have to obtain several sets of keys. This is located on one of the hall monitors in the group that has the brass key. (The first key you get)
Mace of Restoration — [Missable] On your first visit inside the school after defeating the hallway monitor boss you must immediately use the key to unlock the nearby locker.
IN THE GIGGLING DONKEY:
Jester’s Cap — [Missable] Found in a yellow chest in Jimmy’s garage. Also known as the Giggling Donkey.
Elvish Shortbow — [Missable] Obtained automatically after defeating the group of 3 elves in the basement of the giggling donkey after the lights are turned on. Don't light them on fire actually fight them
Wood Elf Cap — [Missable] Obtained from a yellow chest on the second floor of the Giggling Donkey after defeating Jimmy. It’s in the same room.
Wood Elf Gloves — [Missable] Looted from a wood elf in the attic of the giggling donkey.
Crutch of Weakness — [Missable] Obtained off of Jimmy after defeating him on the upper floor of the Giggling Donkey.
Alien Helmet — [Missable] In a purple chest after freeing yourself from the probing machine on the spaceship. It’s behind Randy.
Alien Ray Gun — [Missable] Automatically obtained on the alien spaceship after defeating the first trio of aliens upon escaping from the probing machine. They are directly right of the room Randy is held in.
Alien Suit — [Missable] After taking the elevator down to the room with a tube at the bottom with 2 aliens inside and several platforms and consoles to interface it’s in the purple chest to the left of the elevator.
Alien Gloves — [Missable] Dropped from the space officer in the same room with the third panel to free Randy on the alien spaceship.
Alien Probe — [Missable] After lowering the forcefields it is in a purple chest to the left of the entrance to where Randy is held and you escaped from.
Tinfoil Hat — [Missable] Obtained from the Alien Conspiracy Hobo on the alien spaceship. After you’ve lowered the forcefield you must take the ladder down from in front of the entrance to where Randy is and he is hiding in a pile of garbage.
WHEN YOU'RE RECRUITING THE GOTH KIDS AND HAVE TO HELP RANDY OUT:
Stone Hammer - [Missable] On top of the C.I.A. Building where the Alien ship crashed
SWAT Armored Headgear — [Missable] After breaking into the C.I.A. building where the mall was for the first time it’s on one of the guards killed by the Nazi Zombie.
SWAT Vest — [Missable] After breaking into the C.I.A. building where the mall was for the first time it’s on one of the guards killed by the Nazi Zombie.
SWAT Tactical Gloves — [Missable] After breaking into the C.I.A. building where the mall was for the first time it’s on one of the guards killed by the Nazi Zombie.
SECOND VISIT TO THE SCHOOL:
Basketball — [Missable] On one of the already defeated students inside the cafeteria upon your second visit to the school. To the right of the IN door.
Necromancer Hood — [Missable] On one of the students attacking your fellow human/elf when you first go up to the second floor upon your second visit to the school.
Necromancer Robes — [Missable] On one of the nazi zombie gingers in the room near the entrance to the Boiler Room upon your second visit to the school
Necromancer Gloves — [Missable] On one of the students directly before entering the hallway from the cafeteria upon your second visit to the school
WHEN YOU ARE SMALL:
Gnome Gloves — [Missable] You’ll be forced awake and into a fight with 4 gnomes. After defeating them twice you will be in your room and it will be on one of the defeated underpants gnomes.
Super Bouncy Ball! — [Missable] After entering the hole in your room climb up the first set of wires and it will be on the pouch to your right.
Gnome Helmet — [Missable] After entering the hole in your room climb up the first set of wires and it will be on the pouch to your right.
Gnome Clothes — [Missable] After viewing your parents getting intimate go into the next room. Climb the wires, break the wall to your immediate left, then they will be in the pouch past the 4 batteries.
Gnome Pickaxe — [Missable] After viewing your parents getting intimate proceed to the next room. Go up the wires and to your right. Once you have defeated the 3 rats proceed to the next set of wires and it will be in the yellow pouch before you begin climbing them.
Underpants “Helmet” — [Missable] Whilst on the dresser watching your parents get intimate you will be attacked by 3 gnomes. It will be on one of their defeated bodies
WHEN YOU'RE RECRUITING THE GIRLS:
Poison Grenade — [Missable] Inside of Unplanned Parenthood during the quest for the girls it will be in a drawer underneath the clock between the Records Room and Operating Room A.
Master Razor — [Missable] During the Unplanned Parenthood visit you will have to go into a small hole using the Gnome Dust after being locked in the records room. Just below where the Gnome Nazi Zombies are there is a yellow pouch. It is located inside.
Lawn Dart — [Missable] Yellow Chest on the first floor of clyde’s fortress
Knight Gauntlets — [Missable] Cyclops child in the first room of Clyde’s fortress. He is on the upper level. Same room as the lawn dart’s location
Knight Helmet — [Missable] Yellow chest in the right tower where you see Ike and the pirate girl fighting another Cyclops.
Knight Armor — [Missable] After defeating Craig and his clones it is in the yellow chest in the upper left of the room.
Condom Cap — [Missable] In the yellow chest right after turning on the flash light in Mr.Slave
Vibroblade — [Missable] Nazi Zombie Bacteria inside Mr. Slave next to the iPhone that Big Gay Al calls on.
SIDEQUEST FOR MR.KIM:
Mongorian Bow — [Missable] On one of the mongolian children on the second floor of the Tower of Peace after ringing the gong.