Although there are rather simple rules determining the pronunciation of "the", native speakers quite often deviate from these rules (including, e.g., TV shows). According to the Longman Pronunciation Dictionary,


  The EFL learner is advised to use [ðə] before a consonant sound (the
  boy, the house), [ði] before a vowel sound (the egg, the hour). Native
  speakers, however, sometimes ignore this distribution, in particular
  by using [ðə] before a vowel (which is in turn usually reinforced by a
  preceding ʔ), or by using [ði:] in any
  environment, though especially before a hesitation pause. Furthermore,
  some speakers use stressed [ðə] as a strong form, rather than the
  usual [ði:].


My question is: when native speakers use [ðə] instead of [ði] before a vowel sound, do they do it on purpose or accidentally? If it is on purpose, how do they (typically) decide which pronunciation to use? What is a valid reason to use [ðə] before a vowel sound?


Question: Is "Pick up those blocks" grammatically incorrect?
Answer: "Pick up those blocks" is perfectly correct. The fact that "those" is plural doesn't mean that you can leave out the object, "blocks." How would the child know what to pick up?

There's something off about the sentence "Pick up those," because the antecedent of "those" is missing.


  "Should I pick up these or those?"
  "Pick up those."


is OK. But by itself, it sounds wrong.