My dataset is pretty simple so far:
Questions = Dataset[{
<|"Statement" -> "What is the capital of Switzerland?", "Answer" -> "Bern",
"Incorrect Answers" -> {"Zurich", "Berlin", "Vienna"}|>,
<|"Statement" -> "Who is the king of the jungle?", "Answer" -> "Lion",
"Incorrect Answers" -> {"Giraffe", "Mouse", "Monkey"}|>,
<|"Statement" -> "2+2?" , "Answer" -> "4", "Incorrect Answers" -> {"15", "13", "1e15"}|>}]

If I try the following, everything goes right:
NewQuestion1 = <|"Statement" -> "To be...", "Answer" -> "or not to be",
"Incorrect Answers" -> {"or to eat", "continued", "dummy"}|>;
Append[Questions, NewQuestion1]

Nevertheless, if I delete the dummy answer of the NewQuestion, it will not work:
NewQuestion2 = <|"Statement" -> "To be...", "Answer" -> "or not to be",
"Incorrect Answers" -> {"or to eat", "continued"}|>;
Append[Questions, NewQuestion2]

This issue seems weird since you can declare a data set with uneven lists from the beginning:
Questions = Dataset[{
<|"Statement" -> "What is the capital of Switzerland?",
"Answer" -> "Bern",
"Incorrect Answers" -> {"Zurich", "Berlin", "Vienna"}|>,
<|"Statement" -> "Who is the king of the jungle?",
"Answer" -> "Lion",
"Incorrect Answers" -> {"Giraffe", "Mouse", "Monkey"}|>,
<|"Statement" -> "2+2?" , "Answer" -> "4",
"Incorrect Answers" -> {"15", "13", "1e15"}|>,
<|"Statement" -> "To be...", "Answer" -> "or not to be",
"Incorrect Answers" -> {"or to eat", "continued"}|>
}]

Any suggestions on how to append NewQuestion2 and/or explanations of why this error is happening?

Insert[Questions, NewQuestion2, -1]. All credits to @m_goldberg in the linked Q&A. – seismatica Jul 28 '14 at 18:15