John saw Derek took some sweets from the candy jar.
John saw Derek take some sweets from the candy jar.
John saw [that / :] Derek took some sweets from the candy jar.
(That is, if you don't use "that" - which makes it clear that Derek's 'crime' is described in a subordinate clause - you need to use a colon. Of course, in speech you can't hear a colon, but you can hear the intonation that does the same job - signalling a subordinate clause. And in speech, grammatical niceties like 'subordinate clause' are often ignored, so that it becomes effectively a co-ordinate clause - or, in appropriate language, 'just another sentence - saying what John saw'.)
In an exam it would be safer to use the past perfect:
John saw [that / :] Derek had taken some sweets from the candy jar.
(This changes the meaning slightly; John did not see the event, but he saw the depleted candy jar and concluded that the 'perp' must have been Derek.)
In the case of sentence 2 there is no problem - 'saw' + object + bare infinitive.