I have the problem as well. Slide to answer works only sporadically. Sometimes doesn't slide at all. Sometimes only halfway and then springs back. (And this is only an issue with "Slide to Answer" for incoming calls. "Slide to Unlock" works fine.)
With all due respect to the good people offering suggestions, this is not a hardware issue, nor is it human error or dirty hands. Our phones (mine at least, can't speak for everyone) have never been dropped, never gotten wet and have never been jailbroken.
I currently have an iPhone 4, but the problem existed on my iPhone 3GS as well, as well as a previous iPhone 4 that had screen issues. I have tried restoring the phones and, with each new one, always begin as a new phone, never a backup of an older one. It also occurs with both iOS4 as well as OS3.
Because of this, I can only think of two possible causes: 1) A downloaded App that is making the problem occur, or 2) Something within my iTunes that is making this one feature glitchy.
I'd be curious what apps others have on their phones. Maybe we can find a common denominator.
Here are mine:
Record, NotifyMe, Dropbox, MusicID, Slingplayer, DVR Remote, XM Radio, iHandy Level, Appzilla, Chase Mobile, Citibank Mobile, Flixster, IMDB, ebay, Open Table, CNN, AP Mobile, Angry Birds, Skee-ball, Doodle Jump, Fruit Ninja, Downhill Bowling, Labyrinth 2, Words with Friends, Backgammon, Sudoku, Apple Texas HoldEm.
I should also mention that I have thousands of photos from my iPhoto library. Not sure if this could have an effect.
I've pretty much scoured the internet, and nobody has a good solution yet. Any help appreciated.