I am from Java world and I wonder what is so great about dynamic typing in Python besides missing errors while compiling the code?
Do you like Python's typing? Do you have an example where it helped in a big project? Isn't it a bit error prone?
Do you like it in Python? 

It's part of Python.  Liking it in Python is silly.  

Do you have an example where it helped in a big project? 

Yes.  Every single day I rejoice that I can make changes and -- because of Duck typing -- they are reasonably localized, pass all the unit tests, pass all the integration tests, and nothing is disrupted elsewhere.
If this was Java, the changes would require endless refactoring to pull interfaces out of classes so that I could introduce variations that were still permitted under Java's static type checking.

Doesn't it a bit error prone?

Not any more than static typing is.  A simple unit test confirms that the objects conform to the expected features.  
It's easy to write a class in Java that (a) passes compile-time checks and (b) crashes horribly at run time.  Casts are a good way to do this.  Failing to meet the classes intent is a common thing -- a class may compile but still not work.
How to deal with Python ~ static typing?