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?
I suspect that the vast majority of non-trivial Java programs have dynamic typing in them.  
Every time in Java that you do a cast from Object to an explicit type you are doing dynamic type checking - this includes every use of a collection class before generics were introduced in 1.5.  Actually Java generics can still defer some type checking until runtime.
Every time you use Java reflection you are doing dynamic type checking.  This includes mapping from a class or method name in an text file to a real class or method - e.g. every time you use a Spring XML configuration file.
Does this make Java programs fragile and error prone?  Do Java programmers spend a significant part of their time having to track down and fix problems with incorrect dynamic typing?  Probably not - and neither do Python programmers.
Some of the advantages of dynamic typing:

Greatly reduced reliance on inheritance.  I have seen Java programs with massive inheritance trees.  Python programs often use little or no inheritance, preferring to use duck typing.   
It is easy to write truly generic code.  For example the min() and max() functions can take a sequence of any comparable type - integers, strings, floats, classes that have the appropriate comparison methods, lists, tuples etc.
Less code.  A huge proportion of Java code contributes nothing to solving the problem at hand - it is purely there to keep the type system happy.  If a Python program is a fifth the size of the equivalent Java program then there is one fifth the code to write, maintain, read and understand.  To put it another way, Python has a much higher signal to noise ratio.
Faster development cycle.  This goes hand in hand with less code - you spend less time thinking about types and classes and more time thinking about solving the problem you are working on.  
Little need for AOP.  I think there are aspect oriented libraries for Python but I don't know of anyone that uses them, since for 99% of what you need AOP for you can do with decorators and dynamic object modification.   The wide use of AspectJ in the Java world suggests to me that there are deficiencies in the core Java language that have to be compensated for with an external tool.
How to deal with Python ~ static typing?