Provide your examples of the following using Python lists.

• Nested lists
   
• The "*" operator
   
• List slices
   
• The "+=" operator
   
• A list filter
   
• A list operation that is legal but does the "wrong" thing, and not what the programmer expects.
  Provide the Python code and output for your program and all your examples. 

The code and its output must be explained technically. The explanation can be provided before or after the code, or in the form of comments within the code. For code modification type of questions, always mention or highlight the part which is modified, along with the reason stated, as a code comment.