Anyone has problems with iphone OS 4.0?

I had my iphone 3gs with os 3.12 (jailbroken) for a while and recently upgraded to 4.0
I like the new features and look….
but I am having lots of problems with it
1. battery runs out super fast
2. battery sign on top right corner doesn’t seem to work (when I am almost out of battery…it still says I have 70% battery left)
3. THE MAJOR PROBLEM,,,,,,,,iphone turns off automatically for no reason…goes off when I am in middle of something!! it’s not with particular app….happened to any random app

does anyone have similar problems??and figure something out to fix this problem????