Yes. Very easily, depending on what Joe wants to change.
Edit: additional assumptions.
the universe takes the path of least resistance to validate his statements. Therefore, rewriting the past is only done when no other solution is present. Occam's Razor almost.
Joe has not explicitly stated that no one will notice this ability. Otherwise this post would be a moot point.
If Joe decides to predict/alter the future, it doesn't affect people's memory, and can become suspect. Imagine if Joe is growing up and gets excited for Christmas, as many young children do. Imagine Joe says "Santa is coming! Santa will come down the chimney tonight and bring me presents!" Then imagine how the parents may react when a fat, red-suited, jolly man actually does come down the chimney at night and leaves presents.
It shouldn't be hard for him to simply say something that is unlikely and have it happen. He could predict the next election 10 years in advanced, predict any sports game upset, or predict the winning lottery numbers for a week in a row just by saying so. If any of my friends did that, I would notice pretty fast.
So long as he doesn't limit himself to just altering the past, people will notice. He may make them forget, but someone at some point will notice this gift, at least for some time.
Edit: additional assumptions.
the universe takes the path of least resistance to validate his statements. Therefore, rewriting the past is only done when no other solution is present. Occam's Razor almost.
Joe has not explicitly stated that no one will notice this ability. Otherwise this post would be a moot point.