Touchscreen Protector and Sensitivity I have Samsung Spica I5700 that have capacitive touchscreen, and I used a touchscreen protector.

Recently, I've noticed that the touchscreen often produces erratic movements, for example, if I put my still finger on the screen, the "cursor" will shake vigorously (sometimes very far off). 

This makes the touchscreen very unusable; countless of times I've accidentally flinged the page when scrolling, while touching the screen for small scrolling; countless of times, the screen registered scrolling as a zooming or unzooming; and worse, it often flings to the wrong direction from my swiping direction (indicating a random erratic sensing). Sometimes, when I tried to touch a button/link on the top-left, the screen will detect a click in some other far away button (i.e. one not under my finger). Any games that uses touch intensively also becomes unplayable.

Could this be caused by the screen protector? Since capacitive touchscreen is operated by soft surface of a finger (instead of a pointy stylus), is there any noticeable benefit of using screen protector? or are they just a waste of time and money? do you think peeling off the protector will have a chance of fixing those problems?
To answer you questions: 

Could this be caused by the screen protector?
Possibly.  Take the screen protector off and see if the problem persists.  My screen protector doesn't affect the functioning of my screen at all.  This is going to depend on the particular screen protector (I'm sure there are cheap, bad ones) and the particular phone (they all have different screens and some have calibrations, some dont, some have screen sensitivity adjustment options, some don't).

Is there any noticeable benefit of using screen protector? or are they just a waste of time and money?
Yes there is a benefit, they protect the screen, and no they are not a waste of money. I have scratched/scuffed the hell out of my screen protector and all I had to do was remove it, and put a new one on and my phone was as good as new. Had I not had a screen protector my phone would be unusable now, so for just a few dollars and no performance cost my phones screen is as pristine as the day I got the phone.  That being said, my job and my lifestyle tend to put the phone through a lot of abuse  ;o)

My recommendation: Take the screen protector off and go from there.  If that doesn't work and it's under warranty, bring it back.  

There are so many factors that can affect the touchscreen because it is the basis for all inputs and outputs of the device and troubleshooting can take a while.  I would be surprised if it was the humidity or heat difference between indoor and out, but there are a number of different things that can change from indoor to out and if theres a bug, they may be affecting how your phone operates: GPS, Wifi, reception, Auto-brightness sensor.  

This correlation could also be a coincidence.  It could be a particular app that isn't playing nice with Android and your phones firmware.  

You will need to to systematically isolate the conditions that affect the problems with your screen and the ones that don't, but ultimately it could just turn out to be a bad unit.