1. "What is your biggest gripe with the company?" -- For me, at my current company, this would be exaggerated over-rigidness and glacially slow moving processes (because of checks and emails and re-checks and approvals and and and) when a fast answer/development is required.
2. "How many levels are there in the management hierarchy?" (deep vs flat) -- I tend to prefer flatter hierarchies, which plays into 3:
3. "How much personal freedom do you get?" -- Having more freedom means being more responsible for your work, but also enables you to produce better, faster, more creative stuff. The flatter the company management structure, the better (usually).
A flat hierarchy is not always strongly correlated to personal freedom. I'm 6 or 7 levels below the CEO, but I have a lot of personal freedom because of the management style of my direct manager.
Flat, flexible hierarchies can mask hidden power structures where responsibilities and accountabilities are vague / closed to outsiders. Not always, but something to be aware of...
2. "How many levels are there in the management hierarchy?" (deep vs flat) -- I tend to prefer flatter hierarchies, which plays into 3:
3. "How much personal freedom do you get?" -- Having more freedom means being more responsible for your work, but also enables you to produce better, faster, more creative stuff. The flatter the company management structure, the better (usually).