Minor Fears:
Artwork. Many parts of the preview artwork are "dungeonpunk" in the style of later 3.xE books rather than more classical fantasy/medieval styles. I fear that the flavor of the artwork wouldn't fit my preferences (I like more realistic-feeling art).
Miniatures. I fear that 4E would be more dependent on miniatures and exact tactical movement. This is a minor fear for me as I'm considering moving to minis (or counters) anyway, but I don't really like having my options narrowed.
New races. I am not sure how useful the new races would be in comparison to the previous editions' niche races (gnomes and half-orcs). I don't like gnomes, but I do like half-orcs; but my real concern is how useful the new races would be and how easy they would be to integrate into existing game-worlds. The same goes to the new core-book classes.
Major Fears:
I fear that there would be too many powers/marks/modifiers per combat turn, meaning more paperwork and tracking to do and thus slowing down things significantly.
I fear class ability/power bloat, meaning that there would be too many options to choose from (makes chargen harder) and that creating new classes would involve significant work.
I fear that the rules would be too focused on combat, with other activities such as dungeon exploration, wilderness adventuring, stealth and social situations would receive less attention, especially when race/class abilities/powers are concerned. Take the dwarves for example - Stonecunning (a dungeon-exploration racial ability) is now gone.
I fear that everything would be magical, or have clearly supernatural powers - including low-level fighters. This would push things towards a high-magic setting, and I like mid-magic or even occasionally low-magic. That would also make the rules harder to use for non-D&D settings such as different fantasy, modern or sci-fi.
I fear that the increase in the number of powers/abilities would complicate gameplay, especially when characters such as fighters - formerly the easiest class to play and the refuge of newbies - are concerned.
I fear that the whole re-thinking and re-imagining of the basic setting and flavor elements of D&D would go too far, and slaughter some old standbys in addition to the sacred cows.