Question about parallel clauses

Hi dude,
First of all, the lists that you have mentioned are in an incorrect manner. There should always be a comma before "and" if there are more than 2 items in the list.
So your sentences should look like this below:
"I like to eat, sleep, and drink."
"John likes to swim, bike, and play soccer"

Both the above sentences are parallel. The below sentences are parallel too (Note the comma added before "and")
"I like to eat, to sleep, and to drink."
"John likes to swim, to bike, and to play soccer."

However, the 3rd sentence is parallel only in the second group of examples. You have to repeat "that" in this case.
In order to understand, you could list the items as below:
I like to
- eat,
- sleep,
- drink
OR
I like
- to eat,
- to sleep,
- to drink

Now, the intended meaning of the 3rd sentence is that People used to think 2 things. What are the 2 things?
1. That the earth is flat
2. That boats could fall off the edge of the map.
Here "that" modifies "think". So in your original version (without the extra "that"), the sentence seems to intend that People only thought one thing - that the earth was flat. The other clause - boats could fall off the edge of the map - is some other information, not related with people's thinking.
When you list the 3rd sentence in the above-mentioned fashion, this is what you get:
People used to think
- that the earth is flat
- that boats could fall off the edge of the map
Only when you repeat "that" is when the intended meaning is clear.

Hope this helps. Feel free to ask any more questions.