Here's an exact list of what you should watch. This includes team changes, development episodes, important debuts, and what various others have mentioned.
Episode 469: Following a Maiden Voyage
Episode 670: Two Degrees of Separation
Episode 471: When Pokemon Worlds Collide
Episode 472: Dawn of a New Era
Episode 473: Gettin' Twiggy With It
Episode 474: Different Strokes for Different Blokes
Episode 476: Gymbaliar
Episode 477: Setting the World on its Buneary
Episode 479: Mounting a Coordinator Assault
Episode 480: Arrival of a Rival
Episode 481: A Staravia Is Born
Episode 482: Leave it to Brocko
Episode 483: A Shape of Things To Come
Episode 484: A Gruff Act To Follow
Episode 485: Wild int he Streets
Episode 486: O'er the Rampardos We Watched
Episode 487: Twice Smitten, Once Shy
Episode 488: Mutiny in the Bounty
Episode 494: Getting the Pree Contest Titters
Episode 495: Setting a Not-So-Old Score!
Episode 499: The Grass Type Is Always Greener
Episode 501: All Dressed Up With Somewhere To Go
Episode 502: Buizel Your Way Out Of This
EPisode 503: An Elite Meet & Greet
Episode 504: The Secret Sphere of Influence
Episode 505: A Grass Menagerie
Episode 506: One Big Happiny Family
Episode 508: Top Down Training
Episode 509: A Stand Up Sit Down
Episode 513: Ill-Will Hunting
Episode 517: Dawn's Early Night
Episode 518: Tag! We're It!
Episode 519: Glory Blaze
Episode 520: Smells Like Team Spirit
Episode 521: Tears For Fears
Episode 522: Once There Were Greenfields
Episode 523: Throwing A Track Switch
Episode 528: Joruney To The Unown
Episode 529: Team Shocker
Episode 532: Riding the Winds of Change
Episode 534: Lost Leader Strategy
Episode 535: Crossing the Battle Line
Episode 526: A Triple Fighting Chance
Episode 537: Enter Galactic
Episode 539: Pokemon Ranger and the Kidnapped Riolu
Episode 540: Pokemon Ranger and the Kidnapped Riolou
Episode 541: Crossing Paths
Episode 543: Our Cup Runneth Over
Episode 544: A Full Course Tag Battle
Episode 545: Staging A Heroes Welcome
Episode 546: Pruning a Passel of Pals
Episode 547: Strategy With a Smile
Episode 548: Thief That Keeps on Thieving
Episode 549: Chim-Charred
Episode 551: A Crasher Course in Power
Episode 552: Hungry for the Good Life
Episode 553: Fighting Fear With Fear
Episode 561: Playing the Leveling Field
Episode 563: Battling the Generation Gap
Episode 564: Losing Its Lustrous
Episode 565: Double Team Turnover
Episode 567: A Trainer and Child Reunion
Episode 568: Aiding the Enemy
Episode 569: Barry's Busting Out All Over
Episode 570: Shield with a Tiwst
Episode 572: Sleepless in Pre Gym Battle
Episode 574: A Breed Stampede
Episode 575: Ancient Family Matter
Episode 576: Dealing With Defensieve Types
Episode 578: Steeling Peace of Mind
Episode 579: Saving the World from Ruins
Episode 582: Another One Gabites The Dust
Episode 586: Pursuing a Lofty Goal
Episode 587: Trials and Adulations
Episode 590: Stopped In the Name of Love
Episode 591: Old Rivals New Tricks
Episode 592: To Thine Own Pokemon Be True
Episode 594: Classroom Training
Episode 595: Sliding into Seventh
Episode 596: A Pyramiding Rage
Episode 597: Pillars of Friendship
Episode 598: Frozen in their Tracks
Episode 599: Pedal to the Mettle
Episode 600: Evolving Strategies
Episode 601: Uncrushing Defeat
Episode 604: Gaateway to Ruin
Episode 614: Dressed for Jess Success
Episode 618: Unlocking the Red Chain fo Events
Episode 619: The Needs of Three
Episode 620: The battle Finale of Legend
Episode 622: Mastering Current Events
Episode 623: Double Time Battle Training
Episode 624: A Meteoric Experience
Episode 625: Gotta Get A Gibble
Episode 629: Yes, IN Dee Dee It's Dawn
Episode 630: Playing the PErformance Encore
Episode 631: Fighting IRe with Fire
Episode 633: Flint Sparks The Fire
Episode 634: The Fleeing Tower of Sunnyshore
Episode 535: Teaching the Student Teacher
Episode 638: An Elite Coverup
Episode 639: Dawn of a Royal Day
Episode 640: Win with Easiest of Grace
Episode 642: Last Call, FIrst Round
EPisode 643: Opposites Interact
Episode 644: Coming Full Festival Circle
Episode 645: A Grand Fight for Winning
Episode 647: The Eight Wonder of the Sinnoh World
Episode 648: Four Roads Diverged in a Pokemon Port
Episode 650: An Old Family Blend
Episode 651: League Unleashed
Episode 652: Casting a Paul on barry
Episode 653: Working on a Right Move
Episode 654: Familiarity Breeds Strategy
Episode 655: A Real Rival Rouser
Episode 656: Battling a Thaw in Relations
Episode 657: The Semi Final Frontier
Episode 658: The Borcker is In
Episode 659: Memories Are Made of Bliss
That's 119 episodes. I know this seems like a lot but trust me they are all relevant. I even cut down on some somewhat important episodes like the summer school arc and some Team Rocket development episodes. People say the Sinnoh Saga is filled with filler and crap, but 119 episodes, 62% of the saga are relevant which even surprised me as I was doing the list. Some of the capture episodes and evolution episodes are kinda boring, so you can skip those if you want.