I'ma try to centralize all the really important stuff in one post, in rough order of importance. Plus some stuff that I added on a whim.
General design:
-Consistency. Everyone seems to have trouble with this. I don't mean consistency in which tiles you can stand on and which ones you can't. I don't mean consistency in graphical style. I don't even mean consistency in musical style. I mean all of these things and more. Everything in your level needs to be consistent with everything else in your level.
-Any situation in which the player intentionally kills Juni (with CTRL-R or otherwise) represents a loss of the player's immersion in the level. Whether it's because they stumbled into a void or just because they want to go back to the last save point, it means the damage has been done, and the level is no longer being "properly" enjoyed.
-Don't bore players. In general, this means uninteresting rooms, like long corridors, as well as inexplicably withholding the run powerup.
-A large part of KS level design is preventing the player from getting lost. Extra points if you can make the player think they're lost when they actually aren't. The best way to achieve this is simply to lay out your level in a way that always "funnels" the player in the right direction without explicitly pointing them that way.
-If you need to keep your player from wandering off the edge of the world or climbing up its walls, invisible death tiles are the worst thing to use, followed by invisible non-death tiles, followed by arbitrarily unclimbable tiles, followed by visible death tiles such as an ocean, tied with an overhang large enough to be unclimbable (good examples of making this last one appear "natural" can be seen in The Machine and A Strange Dream).
Gameplay:
-NO DEAD ENDS. EVER. A "dead end" refers to a point in the level where it is impossible to win. This is the worst thing you can possibly do in level design. It's freakishly counterintuitive, extremely frustrating, and just flat-out stupid. Also, an unintentional dead end is just as bad as an intentional one, so make sure to thoroughly test any parts of a level with the potential to be dead ends.
-Have very frequent save points or save-shifts. Difficulty by lack of save points is difficulty by repetition, which is always bad. In "typical" levels like The Machine, one save point every few screens is enough, since challenges are sparse, but levels with many obstacles often warrant many save points on one screen.
-Luck-based or trial-and-error challenges are always bad. Invisible walls and death objects are trial-and-error. A lot of the enemies are luck-based when used improperly; Object 4 in the Plants bank is a frequent offender. Using the retractable spikes in a fashion the player cannot predict is almost as bad as invisible death objects, and arguably more frustrating.
-Don't repeat obstacles. Doing a really tricky jump once might be fun, but doing it five times is not. By the same token, avoid challenges which have been used often in other levels.
-Puzzles should not be trial-and-error. If you can't think of actual puzzles, don't put a "puzzle" in your level.
-Juni's movement is difficult to control with precision, so avoid basing challenges around simple precision, especially if they involve one of the more fiddly components of KS like the umbrella.
-You know Bank 6, Object 5, a.k.a. that green chomper thing, a.k.a. the SandCroc? Stop putting it in every single frupping screen. Thank you.
Graphics, music, and other "flavorful" stuff:
-Remember that point about consistency earlier. Please, please remember that point about consistency earlier.
-If you can't draw/write/compose, don't. Either get better at it or get someone else to do it for you.
-Giving us something that's good and new is generally better than giving us something that's great but old. This is why levels with custom content even exist.
-Tearing the graphics and music out of other games is not only usually illegal, it usually makes for a sucky KS level.
-Anyone remember that "Really Custom Levels" section on the old forum? That one rule about not making your music too loud was there for a reason.