Stardate order is nonsense, as far as I'm concerned. There's no internal consistency between the stardates of the episodes.
I used to think that too, but there is
some consistency if viewed from a large enough scale. Though there are numerous exceptions, a
roughly continuous series emerges rather than just a random mish-mash. I still prefer viewing in straight production order, myself, but...
By sorting episodes first within general production order (pilot, seasons 1-3, TAS, and each movie), by omitting episodes which have no specified stardates, and by dealing separately with those which overlap with other seasons, a general arrangement can be obtained.
The data, omitting episodes which have no stardates specified, and grouping all episodes with cross-season stardates into their own group:
PILOT:
1312.4 Pilot 2 Where No Man Has Gone Before
SEASON 1:
1329.1 TOS-1 4 Mudd's Women
1512.2 TOS-1 3 The Corbomite Maneuver
1513.1 TOS-1 6 The Man Trap
1533.6 TOS-1 8 Charlie X
1672.1 TOS-1 5 The Enemy Within
1704.2 TOS-1 7 The Naked Time
1709.1 TOS-1 9 Balance of Terror
2124.5 TOS-1 18 The Squire of Gothos
2712.4 TOS-1 10 What Are Little Girls Made of?
2713.5 TOS-1 12 Miri
2715.1 TOS-1 11 Dagger of the Mind
2817.6 TOS-1 13 The Conscience of the King
2821.5 TOS-1 14 The Galileo Seven
2947.3 TOS-1 15 Court Martial
3012.4 TOS-1 16 The Menagerie
CROSS SEASON 1 AND SEASON 2:
3018.2 TOS-2 30 Catspaw
3025.3 TOS-1 17 Shore Leave
3045.6 TOS-1 19 Arena
3087.6 TOS-1 20 The Alternative Factor
3113.2 TOS-1 21 Tomorrow Is Yesterday
3134.0 TOS-1 28 The City on the Edge of Forever
3141.9 TOS-1 24 Space Seed
3156.2 TOS-1 22 The Return of the Archons
3192.1 TOS-1 23 A Taste of Armageddon
3196.1 TOS-1 26 The Devil in the Dark
3198.4 TOS-1 27 Errand of Mercy
3211.7 TOS-2 46 The Gamesters of Triskelion
3219.8 TOS-2 31 Metamorphosis
3287.2 TOS-1 29 Operation - Annihilate!
3372.7 TOS-2 34 Amok Time
3417.3 TOS-1 25 This Side of Paradise
SEASON 2:
3468.1 TOS-2 33 Who Mourns for Adonais?
3478.2 TOS-2 40 The Deadly Years
3497.2 TOS-2 32 Friday's Child
3541.9 TOS-2 37 The Changeling
3614.9 TOS-2 36 Wolf in the Fold
3619.2 TOS-2 47 Obsession
3715.3 TOS-2 38 The Apple
3842.3 TOS-2 44 Journey to Babel
4040.7 TOS-2 43 Bread and Circuses
4202.9 TOS-2 35 The Doomsday Machine
4211.4 TOS-2 45 A Private Little War
4307.1 TOS-2 48 The Immunity Syndrome
CROSS SEASON 2 AND SEASON 3:
4372.5 TOS-3 57 Elaan of Troyius
4385.3 TOS-3 56 Spectre of the Gun
4513.3 TOS-2 41 I, Mudd
4523.3 TOS-2 42 The Trouble with Tribbles
4598.0 TOS-2 49 A Piece of the Action
4657.5 TOS-2 50 By Any Other Name
4729.4 TOS-2 53 The Ultimate Computer
4768.3 TOS-2 51 Return to Tomorrow
SEASON 3:
4842.6 TOS-3 58 The Paradise Syndrome
5027.3 TOS-3 60 And the Children Shall Lead
5031.3 TOS-3 59 The Enterprise Incident
5121.0 TOS-3 63 The Empath
5423.4 TOS-3 72 The Mark of Gideon
5431.4 TOS-3 61 Spock's Brain
5476.3 TOS-3 65 For the World Is Hollow and I Have Touched the Sky
5630.7 TOS-3 62 Is There in Truth No Beauty?
5693.4 TOS-3 64 The Tholian Web
5710.5 TOS-3 68 Wink of an Eye
5718.3 TOS-3 71 Whom Gods Destroy
5725.3 TOS-3 73 The Lights of Zetar
5730.2 TOS-3 70 Let That Be Your Last Battlefield
5784.2 TOS-3 67 Plato's Stepchildren
5818.4 TOS-3 74 The Cloud Minders
5832.3 TOS-3 75 The Way to Eden
5843.7 TOS-3 76 Requiem for Methuselah
5906.4 TOS-3 77 The Savage Curtain
5928.5 TOS-3 79 Turnabout Intruder
5943.7 TOS-3 78 All Our Yesterdays
The animated series can be included if its stardates are similarly handled by season. First off, any TAS episodes which overlap TOS seasons 1 or 2 must be omitted:
1254.4 108 The Magicks of Megas-tu
3183.3 203 The Practical Joker
4187.3 114 The Slaver Weapon
This still leaves a massive overlap with TOS season 3. While there are differences in the TOS Enterprise/crew and the TAS Enterprise/crew, I'm willing to combine TOS season 3 and the remaining TAS season 1 episodes (since all of TAS season 1 would otherwise be omitted):
4978.5 110 Mudd's Passion
5143.3 106 The Survivor
5267.2 112 The Time Trap
5371.3 103 One of Our Planets is Missing
5373.4 102 Yesteryear
5392.4 105 More Tribbles, More Troubles
5483.7 104 The Lorelei Signalof females.
5499.9 113 The Ambergris Element
5501.2 115 The Eye of the Beholder
5521.3 101 Beyond the Farthest Star
5554.4 107 The Infinite Vulcan
5577.3 111 The Terratin Incident
5591.2 109 Once Upon a Planet
5683.1 116 The Jihad
The following TAS season 2 episode is omitted for overlap with TOS:
5275.6 204 Albatross
Leaving the following episodes to represent TAS season 2's stardates:
6063.4 205 How Sharper Than a Serpent's Tooth
6334.1 201 The Pirates of Orion
6770.3 206 The Counter-Clock Incident
7403.6 202 Bem
MOVIES:
7412.6 Star Trek: The Motion Picture
8130.4 Star Trek II: The Wrath of Khan
8210.3 Star Trek III: The Search for Spock
8390 Star Trek IV: The Voyage Home
8454.1 Star Trek V: The Final Frontier
9521.6 Star Trek VI: The Undiscovered Country
Thus, the "pure" stardate ranges (which are the majority within each segment and which improved over time, except for the TOS-3/TAS-1 overlap):
1312 Second pilot
1329-3012 TOS first season
3468-4307 TOS second season
4842-5943 TOS third season & TAS first season
6063-7403 TAS second season
7412 Star Trek: The Motion Picture
8130 Star Trek II: The Wrath of Khan
8210 Star Trek III: The Search for Spock
8390 Star Trek IV: The Voyage Home
8454 Star Trek V: The Final Frontier
9521 Star Trek VI: The Undiscovered Country
This provides an overall smooth progression from 1xxx to 9xxx.