Related to this question: How many times was Obi-Wan less than honest with Luke?
In A New Hope, when Luke asks 3PO to tell him about the rebellion, the droid replies:
I'm not very good at telling stories.
But in Return of the Jedi, he recounts the events of the entire trilogy up to that point in a spellbinding manner, complete with almost perfect sound effects. Clearly, his statement in ANH wasn't entirely true.
Later, when R2 refuses to play the video of Leia for Luke, 3PO conveys R2's lie that the recording had disappeared. When Luke leaves the room, 3PO says:
Just you reconsider playing that recording...
which makes it clear that he had covered for R2 by misleading Luke.
This calls his trustworthiness into question, in my opinion, so I am forced to ask: