everyday life - Backyard experiments to falsify the Flat Earth theory

I recently became aware that the flat Earth theory still exists in the 21st century, and has colored the views of a friend of mine. Roughly speaking, the tenets are:

• The Earth is a flat disk, with the south pole blown up into a circular "ice wall" where one would expect Antarctica to be.

                                        

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  The sun and moon are either spheres or disks floating above the earth and moving in a spiral pattern with the seasons.

  
  


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  NASA is part of a conspiracy to conceal the truth, and sends us animations and faked photo shoots.

  
  

The Flat Earth Theory is a scientific theory, in the sense that it makes falsifiable predictions about the universe that can be seen to match observation (or not). What are some good arguments or backyard experiments that could convince a layman that in fact the Flat Earth Theory is false?

A similar question and useful related reading is What is the simplest way to prove the Earth is round?, but it focuses more on the theoretical and conceptually simple side, applicable to the proverbial "numskull cousin". This question is more focused towards convincing a doubtful scientific person using (preferably low-tech) experiments and observations.