Ditto all the above.
Also when work is not divided evenly among partners (allowing, of course, for easier workloads for those otherwise busy maintaining and especially growing the business. The key here, of course, is busy. Differences in workload and compensation among partners generally do not equilibrate or even stabilize with time. If you can't justify it now, you will grow to despise it later.
Unexplained age gap between partners and minions, with no/few mid-level partners in between. That's churn-and-burn until you prove otherwise.
Prolonged time to partnership (greater than three years), regardless of the very unique and extra-special reason invariably given. There is no reason other than milking you.
Weak and/or shrinking revenue base. No one sharp really minding the business. Probably the most overlooked red flags of all.
Repellent personalities. This is pathology, so a given baseline weirdness goes without saying. I'm talking someone who makes your skin crawl, which is actually an evolutionary survival reflex if you think about it. Ditto corrupt partners engaging in corrupt and/or dubious activity. There is no honor among thieves.
Basically you have to stop thinking like a newbie fixated on deliberately distracting but temporary fluff, like the nugatory goodies you may or may not get during your trial period. Think about what could cause you to quit or lose your position five, ten, fifteen years down the line.
It goes without saying that none of this matters with non-partnership positions, because you shouldn't be there long enough for any of this to make a difference, anyway.