I think you need to be clear with yourself on what reaction you want and why you want to complain. Here's some cases that might be true and some ideas for how to get what you want.
Venting
I honestly think that giving people a place to vent off steam about previous conditions and past issues is good - to a point. People need a place to talk about negative stuff, and for some, it will come out as complaining - particularly the first time you get something off your chest. For those of us who think by talking, a trusted confidant is a must.
Things to think about when venting:
First perception - Don't let the venting be the first perception a new manager has of you. Let the first perception be the good stuff - your enthiasm for a change, your hopes for doings better in the future, current good work that you are doing. Get yourself a reputation as a can-do person.
Trust - you really can only vent to someone you trust. Pick your allies. Not every manager is a good venting-recipient - and trust is a hard thing to describe. Certainly if previous history leads you to believe that the manager won't keep your disclosures private, the don't vent. But other points of trust building are very personal.
Set expectations - coming right out and saying "I need to vent, do you have a sec?" is a fine way to go. Usually 1 on 1s is a safe space for this, or ask to book a meeting. The big thing being that anyone can only take so much whining and complaining in a day, and if the person in question just endured 3 other rounds of stress or pressure, then you may get an undeserved negative response that is far more forceful than you expect. Let the listener have a say in when and where you vent.
Try to end with a fix - if you can, try to end with a "next time we'll do X better..." idea. I'm not so sure you can ALWAYS have a better answer but try for it anyway. A key to making change is to always keep trying.
Limit your venting - if you come back to the same pattern or single frustrating incident over and over, it's time to let it go. I don't care how much it bugs you, there's limit to the number of times you can vent about the same thing until you have just agree to ignore it, deal with it, or change jobs.
Trust Building
Another reason to talk about past mistakes with old bosses is to give yourself a sense of faith that the new bosses will be better. I'd call this baseline setting rather than complaining. Don't state the issues of the past as a complaint or a rant, ask questions about causation and ask open ended questions. Examples:
What's your thought about overtime? What is "too many" hours? When is it OK to put in that extra effort and how often do you think it is reasonable?
How do you want to hear status?
What decisions do you want input on?
How do you want to communicate? What to you is a "hot issue" that needs urgent escalation?
Those are nice an open ended, but also if you've had specific issues leading to a lack of trust, find a way to ask in a similar situation what would the new bosses do?
This can lead to a more frank discussion. For example, I got a question in an interview at one point that was somewhat analagous to "have you ever seen the sky turn purple?" - my response was "I've never seen it, I can't even imagine a case of it - have you had a purple sky issue?" which led to some pretty specific cases of purple skies that were shocking and unpleasant. When probed, feel free to talk about your own past purple sky issues, and why you found that to be a real problem (if it isn't obvious).
Generally, though, let the boss ask the question, if they don't, take their answers at face value. Getting to a point of demanding a promise isn't going to serve you well.
Can we change?
If some really bad decisions put into effect a bad precedent or process, it's a good time for a change. Some ideas for getting the most bang for the buck:
limit your focus - if everything is broken, find the 1-5 worst issues and focus in, one or two at a time.
change is small - find some "if we just did a few things differently..." cases and go for them. Don't try to rebuild the company from the ground up on day 1.
Ask questions - "We've done X, Doing Y is better/faster/nicer and achieves the same/better outcomes... mind if we do Y?"
Keep it short - the history of how you came to X really doesn't matter. What X is, why it isn't as good as Y, and what negative impacts it has are the range you need to discuss.
Choose your language - When it comes to the difference between "identifying a bad choice" and "complaining about former choice-makers", the difference is largely in the choice of nouns. "This choice is bad" vs. "This manager made a bad choice" - probably the same thing, but the first highlights the choice, not the person, and focuses the attention on what can change.
Offer and easy path - day 1, with little experience, any path to change is best as a "baby step". You don't trust them yet, they don't trust you - taking on faith that the company should make huge risky changes at this point will not be easy, no matter how well you present the option.
The Fan is over here, the flying excrement will be arriving from this vector...
There are times when you know for sure that new management is walking into a mess. There's no way to fix it, there is just surviving it. Having grace, being polite, and keeping your morale from tanking is about all you can do.
Yes, it's polite to warn them, but do it once and leave it be. Don't be Eyore (sitting in a corner, believing everything is doomed to failure). And how forceful you are has something to do with how much you like, trust and respect your management.
It's another time for booking a closed door meeting. Phrase it as an update walking through the key events that lead to the mess, and your rationale for what the fallout will be. Have some survival ideas, and some best/worst case estimates. This isn't venting, this is letting management know that some projects will torpedo, whether they like it or not. Stay out of judgements and accusations and "what ifs" - "Management was short sighted" vs. "this was a poor decision in light of long term goals" - "if only we had done X, we would not be failing so miserably" vs. "the decision to Y instead of X lead to Z outcome, worsening our stance". Small rephrasing, but important.
Finish with expressing your willingness to help, even if you are lost on how to make the bad situation better.