Everyone makes mistakes in playing go. Beginners make few correct moves ... amateur dan players probably make some, since otherwise they'd be losing more than 100 points per game to best play (which seems unlikely).
It seems useful to separate out early mistakes everyone has to get past in learning the game, from those that persist certainly in all kyu-level players. That is, we need a category for mistakes that aren't novice errors (running out of liberties, being cut, groups dying of neglect of eyes and territories broken into). It therefore makes sense to reserve 'amateurish' for these remaining, tenaciously-rooted mistakes.
Examples are certainly:
- heavy play
- aji keshi
- backing down from ko fights
- not counting, and playing so as to make that obvious.
Confused: One could add to the list:
- playing shape-ish looking moves while ignoring the simple efficient ones.
- playing the wrong joseki or not knowing when to deviate from the joseki.
Andre Engels: A typical mistake that leads to one's play being called "amateurish", is playing the right shape at the wrong time. That is, knowing some sequence and playing it, not realizing that in the specific position at hand it is completely wrong from a strategic point of view. It's actually the same error as the second that Confused mentions, but shows itself not only in joseki but also later in the opening and in the middle game.
 This is an exaggeration. Certainly by 15k, players are already playing *some* correct moves: there are situations where the correct move is quite clear, such as in semeais and life-and-death (assuming the groups involved are large enough that killing/living is correct), and large sente endgame plays. These make up a minority of moves, but it's not clear to me how often even professionals play the mathematically correct move.