I really enjoy watching TV episodes in the order they were actually filmed, as opposed to network order. The production number codes for most TV shows indicate the order in which episodes were filmed. The numbers for Out of This World are extremely difficult to find as none of the episode guides available online seem to include them. I managed to find the production numbers for all seasons except for the final one. These were obtained through online U.S. copyright records. For some reason, the final season is not listed. Thus, I only have a few of those numbers obtained by looking at the first page of scripts sold on Ebay (which is also where the taping dates came from for all the episodes I've included those for). Does anyone have the production numbers for the final season and can fill in the gaps?

This is what I have:

15301 Evie's Birthday
15302 Nightmare (Taped March 20, 1987)
15303 Till Then (Taped March 27, 1987)
15304 Every Beano Has His Day
15305 Anniversary
15306 Broadway Danny Derek
15307 Illness
15308 Baby Talk (Taped May 15, 1987)
15309 Uh-oh, Here Comes Mom (Taped May 22, 1987)
15310 Box is Missing (Taped June 5, 1987)
15311 Beano's New Diet Clinic (Taped June 12, 1987)
15312 Evie and the Young Astronauts (Taped June 19, 1987)
15313 Playing with the Power (Taped June 27, 1987)
15314 Evie, Get Your Basketball
15315 Pen Pals (Taped July 16, 1987)
15316 Fifties Mom (Taped July 24, 1987)
15317 Deuling Mayors
15318 Russians are Coming (Taped August 14, 1987)
15319 A.K.A. Dad (Taped August 21, 1987)
15320 Mosquito Man - the Motion Picture
15321 I've Got a Secret
15322 Boy Crazy
15323 To Tell the Truth
15224 The Three Faces of Evie

0201 Evie's Birthday Wish
0202 Blast from the Past
0203 Career Crunch
0204 Should Old Acquaintance Be Forgot?
0205 Evie's First Kiss
0206 Princess Evie
0207 Old Flame
0208 Guess Who's Coming to Earth? (Taped October 21, 1988)
0209 Go West, Young Mayor
0210 Close Encounters of the Nerd Kind (Taped November 11, 1988)
0211 Incredible Hunk (Taped November 18, 1988)
0212 Secret of Evie's Success
0213 Evie's Two Dads
0214 Honest Evie
0215 Too Many Evies
0216 Pupil's Court
0217 Queens for a Day
0218 Futile Attraction
0219 Beano, the Kid
0220 Evie Goes Hollywood
0221 Amazing Evie
0222 Frisky Business
0223 Star Dog
0224 Whose House is it, Anyway?

0301 Cinderella Evie
0302 Evie's Secret Admirer
0303 Around the World in 80 Minutes
0304 A Froggy Day in Marlowe Town
0305 Evie's Driver License
0306 It's a Cruel World
0307 Eviegeist
0308 Evie's Sweet Sixteen
0309 Bring Me the Head of Donna Garland
0310 Evie's Magic Touch
0311 Evie/Stevie (Taped June 23, 1989)
0312 The Rocks That Couldn't Roll (Taped June 30, 1989)
0313 Hair Today, Gone Tomorrow
0314 Four Men and a Baby
0315 Evie Goes for the Gold
0316 Cowboy Kyle, Man of Granite
0317 One in a Million
0318 Evie's Double Trouble
0319 Evie's Yuppie Love
0320 The Garden of Evie
0321 My Mother, the Con
0322 A Kinder, Gentler Mayor
0323 Diamonds are Evie's Best Friend
0324 Goodbye, Mr. Chris

0404 Evie's False Alarm (Taped August 3, 1990)
0419 All about Evie (Taped December 14, 1990)
0420 Evie's Three Promises (Taped December 21, 1990)