There is a lot of great advice of the usual sort floating around - talk to current grad students and postdocs about Department, Program and Lab culture. Median time to completion*. So I won't repeat that.
But here's one thing you may not hear about.
Ask the Program Director for the past two 5-year reviews of the Program. Yes, graduate training programs get peer reviewed on a periodic basis. Every 5 years in my limited experience.
Ask to see the review. Absent that ask for the top five most serious criticisms. In fact you should ask this latter question if anyone who interviews you to get a sense of how much the Program is integrated vs ad hoc.
Here's another important question to ask the interviewing faculty: "Who are the most recent 5-10 faculty appointments to come from your Program alumni?" The key here is to ask it on the spot so they can't look it up.
The most important thing here will not be the actual-factual answers. It will be how the faculty respond to your inquiries.
*Please tell me every prospect asks about the median time to PhD?
UPDATE: I meant this as a step to take after you are invited to interview or offered admission. A step for you to take to help decide which program to attend. Although I suppose even if you only get one offer it is helpful to know what to expect or watch out for.