There are 25 places of power (25 points). You stop getting ability point by level when you reach level 70 (69 point). There may or may not be a level cap and if there isn't I wonder when you stop gaining buffs so you dom't become too powerful. As far as I know this is the most accurate information I gather form multiple decent rouses even though some had different opinions/statements.
Since the wikis for Witcher 3 are not as good as they should be and even though a game is out for a year now there is still a lack of some basic information and statistics on the game so I tried to figure out how many ability (skill) point a player can receive in total.