I'm just wondering what issues are supposedly going on with it because we haven't encountered anything significant. It would help to know to fix it before it happens.
It very much depends on the particulars of each system. However, one of the most common problems is too much freedom to swap low-powered spells for higher, or vice versa. I think high to low is usually more of a problem than the other way, but both can happen.
Take a naive power point system initiated off of AD&D spell slots. Convert all 1st level slots to 1 point, 2nd level to 2 points, etc. Suddenly, a higher level caster can convert a few lower level spells into an extra 9th level spell. Then someone tries to fix the worst of the low to high conversion by charging 1 point for 1st, 3 points for 2nd, 5 points for 3rd, etc., with each spell slot giving the corresponding amount. Now, suddenly, a single 6th level slot lets a caster do a max magic missile all day long.
But mainly, it takes a system that is already very generous strategically and makes it even more generous and flexible tactically. In a game designed with power points from the ground up, you'll often see some variation on scaling such that the caster can be
reasonably flexible with low level, modest effects, but really has to sacrifice and dig for the bigger stuff--and the scaling is usually fairly steep after a point, often with unpredictable risks. This often leaves the caster bereft of magic when they try too much, but even that isn't such a big deal in a skill-based system, where the caster has other things to use.
D&D is
already prone to the wizard being balanced on a razor edge between hopeless drag and terribly over-powered. Power points tend to exaggerate such issues anyway. That's also, by the way, why power point house rules for D&D tend to work better for a particular group when they stick to a relatively narrow level range. Even the AD&D naive implementation isn't so bad between 3rd and 9th level, especially in certain playstyles.