1. Stories in areas aside from Canterlot, the Crystal Empire, or Ponyville. There are so many places mentioned by name, but aren't given a lot of exploration (Manehattan, Fillydelphia, and Baltimare being three of them). It would be fantastic to see the lives of those cities and see how the citizens there adapt.
   
2. New character interactions. One of season two's biggest strengths is putting characters of various personalities into groups of three (and succeeding with them). Putting Your Hoof Down had Fluttershy with Pinkie and Rarity, whereas Dragon Quest had Twilight, Dash, and Rarity. Twilight Sparkle communicates a lot with Spike, Pinkie, and Rainbow Dash, but not so much with Fluttershy (not since season one, anyway). It'd be great to pair Twilight and Fluttershy into one episode and have them communicate and become even closer friends than it already is.
   
3. An episode where Twilight truly reflects on her friendship. The closest we've seen was Return of Harmony, Part 2 and Magical Mystery Cure, but they were merely smaller scopes within a much bigger plot. An entire episode reflecting her growth would be better.
   
4. Another Scootaloo episode, but not with Rainbow Dash. She may be Dash's protégé, but she's a character where most of who she is surrounds with her and the Cutie Mark Crusaders. What about her relationship with the rest of Ponyville, like Cheerilee, Applejack, or even a background character like Derpy?
   
5. A Silver Spoon-centric episode, and maybe one where she can finally step out of Diamond Tiara's shadow and become a character of her own. She doesn't have a lot of character growth to individualize her, and the hint of development she had (her being the first to applaud Granny Smith) was erased from the chalkboard. Have her grow into a genuine, three-dimensional character!
   
6. A Rarity episode.
   
7. Good Spike-centric episodes. His two episodes in season three suck because they made him an out-of-character soul, which is a shame because his smaller roles helped him grow. And it IS possible for his episodes to be genuinely good, evident by Secret of My Excess and Dragon Quest.
   
8. Trixie attaining a more secondary role. With her much more confident and mentally healed, explore her trials, failings, and triumphs. If creating a show for an audience, but can be troublesome, have her get some help from the Mane Six (maybe Twilight) or Snips and Snails (but by treating them as genuine characters instead of slaves).
   
9. More tertiary roles for the background characters. One drawback in season three was how the background characters' roles diminished compared to seasons one and two; Wonderbolts Academy, Crystal Empire, and Apple Family Reunion had them doing something besides merely being there.
   
10. Speaking of which, have Derpy reappear more (WITH her derpy eyes!). The season finale was a great start; I hope to see more of her in season four!
    
11. A more conservative role in growing the characters. Season three's biggest issue is making the character participate in bold roles way too quickly, inorganically developing the characters occasionally. If going bold, foreshadow it better. Don't cram every single nook and cranny in the episodes, because that's one easy way to produce rushed episodes.
    
12. SLOW—THE HELL—DOWN! One Bad Apple, Keep Calm and Flutter On, Games Ponies Play, and Magical Mystery Cure had episodes progress so quickly that the hints get easily lost or the problems get solved way too quickly and unrealistically. Much better pacing is key.
    
13. At least one Cutie Mark Crusader getting her cutie mark. It's been three seasons with little to no progress, and I think it's time to foreshadow a new cutie mark. Again, though, foreshadowing within a proper pace is important to make the story convincing.
    
14. Echoing Citrus King46 in another post: focus on the characters without using the usual tropes. A good FIM episode isn't merely about overcoming a flaw anymore. It's also about creating conflict and using the characters' strengths and/or equal balance of the characters' strengths and flaws to solve them in a well-told story. Examples include:
    
    1. 
       
    2. Rainbow Dash: Without focusing on her pride or arrogance and more on her confidence, sincerity, and loyalty. Wonderbolts Academy hinted this, but it mostly focused on a whole balance, her pride early in the episode, her doubt in the middle, and loyalty to her family in the end. Sonic Rainboom is another great example, showing her fear of failure.
       
    3. Fluttershy: Less focus on her social anxiety and more on her kindness and care for others. Keep Calm and Flutter On showed a side from her barely seen in the series: her patience and tenacity. She let Discord beat her and then flipped the tables by forming a bond that can't be broken.
       
    4. Scootaloo: Less on her idolization of Rainbow Dash and want to fly and more on her other strengths, such as her growth in her bravery and love for extreme sports.
       
    5. Twilight: Less on her impatience and cracking under pressure and more about trying to accomplish tasks with a calm, fair conscience. Winter Wrap-Up's an excellent example of that.
       
    6. Spike: Less focus on greed and jealousy and more on his determination, bravery, care for his friends (i.e., Lesson Zero), and will to fulfill his tasks right from beginning to end.
       
    7. Rarity: Many of her episodes focused on the high life or dresses. Sisterhooves Special was about her relationship with Sweetie Belle, and A Dog and Pony Show focused on using her intellect and intelligence to escape the Diamond Dogs.
       
    8. Applejack: Less about the farm life and stubborn pride. Apple Family Reunion did half of this, which was trying too hard to make things right and even better. What would be great is have her do everything right and then succeed so well that maybe she can repeat it, only to make her work too hard as a result. You get the semi-results from Applebuck Season, but without the pride getting in her way.
       

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Source: What do you want to see in Season 4?