I no longer bother to download levels which don't have both all-exclusive tilesets and all-custom music. (I should point out that by "exclusive" I mean "made specifically for the level," and by "custom" I merely mean "not the default tracks that I've heard two thousand times.")
I've seen the default tilesets and the good public tilesets used and overused to the point where the sight of them annoys me. I consider the act of laying out screens and actually designing a level to be trivial at its best, and thus the meat of any KS level is its custom content.
This is an attitude that I developed rather quickly after releasing my second level to the public. I looked at my level and at other levels and realized that, on the whole, they felt the same.
Hence my "new" (and the quotes are very appropriate here as work on it started two years ago) level that I may never finish due to the sheer quantity of work that it encompasses, combined with my general laziness. But to me, it's better than releasing something else that's cruddy.
My advice to any new users of the editor: make levels with default content, but don't release them. Eventually you'll get tired of making levels that all look and feel the same, and will want to make custom tilesets and such; that time is when you should start doing so, and hopefully not be wearied by having "too many levels out there already."
But then again, that's just my advice. It's obvious that my opinions don't coincide with those of other people here, especially with regards to custom KS levels.
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And as far as things that annoy me aside from unoriginal tilesets/music: not knowing where to go. I hate completely linear levels, but I also hate having to wander, not exploring the world, but rather looking for the next arbitrarily placed powerup. Levels should point you in the right direction (but not too much or they do indeed become linear). For instance, in A Strange Dream, if you don't yet have the climb powerup, your surroundings are shaped such that you'll be funneled gradually towards it regardless of what direction you go.
Also, the use of the retracting spikes in the Traps bank is usually unnecessary and unfitting; prefer drawing spikes into your tileset, and putting kill objects on those. It looks much, much better in most circumstances, and falling into retractable spikes that you didn't know would be there is second only to rampant SandCrocs in terms of annoying things that constantly crop up in poorly conceived level designs.
NESgamer, those sound more like crippling, playability-ruining problems than nagging flaws.