What's laughable is talking about the facts of how Floyd was killed when there are 3 different official versions, all that disagree. He was Public Enemy 1 at his death and Edgar moved Dillinger up, so yes the order is wrong in the movie.

No, we will not read the book because we will watch the movie and leave it at that.

Facts are for documentaries. A movie like thiseven if it's based on factis a work of fiction. That being said, it was a good book and it would make a good miniseries. And that's probably because a miniseries is what it was originally supposed to be, as I now see Petronius Arbiter II pointed out.

Flow. Introducing Pervis as the man who got Floyd and will get Dillinger is a key point of introducing him to the audience.

noand one of the biggest cock-ups of all is the portrayal of the Little Bohemia episode and shoot-out, and having Purvis men kill Baby Face Nelson as part of that complete Fubar.
From memory, they killed or captured no one major that they were after in the bohemia raid, and killed at least one or two innocent men in that car they opened fire on without even knowing who the hell was in it.
They were from a nearby timber or agro work-camp, just there for a few drinks.

Why would they do this? It makes no sense to me.
Because, despite the title and the credits' nod to Bryan Burrough's book, it's not really about the "public enemy era" gangsters as a whole, it's about John Dillinger. Hence, they monkey with the historical order of deaths for the same reason John Milius did in 1973: it makes good dramatic sense to save Dillinger's death for last.
Just the same as it makes good dramatic sense to invent a fictional meeting between Dillinger and Purvis in the Tucson jail. Never happened in real life, but it's one of the better scenes in this film.
"I don't deduce, I observe."

Dillinger, Floyd and Nelson were all killed in 1934, in July, October,and November respectively. I don't understand why this otherwise-fairly accurate film got the sequence of their deaths wrong, with Floyd being portrayed as the first to die, then Nelson and lastly Dillinger.
Why would they do this? It makes no sense to me.

Hmmmm Whatta we got here?
If you rely on Burrough's book, and only Burrough's book, for your "understanding of the times and events of those years," you're not going to get all that clear an understanding of the Dillinger saga. It's a very good book, but there are better Dillinger books out there.
"The killing of Floyd is laughable compared to the real events and it was Purvis' secretary that stopped the brutal interrogation of Billie"
I don't have a problem with the smallish inaccuracies of the Floyd death scene. They serve a valid artistic function, even the misplaced timing on the calendar. The killing of Baby Face Nelson, on the other hand, was done very badly in "Public Enemies," and contributed to by far the worst historical inaccuracy in the whole film, the portrayal of the Little Bohemia shootout as an FBI triumph.
Purvis' (female) secretary
initiated
the end of the unconstitutional interrogation of Billie Frechette, but she didn't have any power to actually stop it. Only Melvin Purvis did. To the degree this scene is inaccurate i.e. not very much it's not inaccurate in the same way you think. It would have been a nice touch to include the secretary's input, though.
"The scene where they try to decide what movie he is going to see is a freaking joke. I mean there is so much wrong with the facts of the movie it would take me days to list."
Sources? What exactly do you think is wrong with that scene? Perhaps you should know that we have extensive documentation about what was said to law enforcement officers before they went out to stake out the two theaters.
Not all of that made it into Burrough's book;
see above: there are other and better books out there.
I don't know if anybody actually said out loud that Dillinger would choose a gangster movie over a Shirley Temple movie, but many of them
had
to have been thinking it. If this was added, it seems a perfectly valid use of artistic license.
As for the "long list," I already started a "History Versus Hollywood" thread back in 2009, a day or two after PE hit the theaters. It fell off the back end of IMDb's "Public Enemies" board a long time ago. I may repost it soon.
My main conclusions from that initial study, and later, have been:
(a) For all its inaccuracies, this is still by far the most accurate Dillinger film yet made. Mann and the other writers
did
do a damn good job of portraying the complex and charismatic character of John Dillinger. Billie Frechette, too.
Melvin Purvis, OTOH, not so much. And I sure would have liked it if this movie had made it clearer just what a self-serving scoundrel J. Edgar Hoover was. No filmmaker has ever done justice to Hoover's villainy. Clint Eastwood and Leo didn't do it either.
(b) The only inaccuracies that significantly harmed the quality of the movie were the above-mentioned Little Bohemia resolution, and the portrayal of Frank Nitti and the Cosa Nostra-based Chicago Outfit as being rather more involved in the Dillinger saga than they really were. Well, hey, Michael Mann is from Chicago. He's a bit obsessed with the gigantic legacy of Al Capone. (Me, I'm not. I'm from John Dillinger's home turf.)
You do know this is not a documentary, don't you?
"The real stories of all the Midwest gangs is so much more interesting like when Dillinger and Pierpont lived out of a red panel truck for days/weeks." Let's stop right there. Well,
duh.
Of
course
real history is far more interesting, for those of us who enjoy reading history books.
You do know this is the Internet
Movie
database, don't you?
And you do know this is not a miniseries, don't you? "Public Enemies" started out its life as a plan for a
fictional
HBO miniseries of the kind you (or I) might like to see. Then HBO decided they didn't want to invest a billion dollars in it, so they set their researcher Bryan Burrough free to use
their
title for the nonfiction book he wanted to publish from his HBO-commissioned research notes. Which at the time were still HBO's legal property, by the way.
Now, if you think you can do better at making a comprehensive miniseries out of the John Dillinger saga, please do so. All you need is a billion dollars.
Oh, BTW, that was Homer Van Meter in that red panel truck with Dillinger. Not Harry Pierpont, who was already well on his way to the electric chair.
And what they were doing in that truck had nothing much to do with John Hamilton, who was dead within less than a week of being shot, and Dillinger and Van Meter's taking him to Volney Davis' place, which didn't take them all that long to find.
"PS Purvis was so nervous that night he was unable to light his cigar and did not do it with one easy stroke and did not fire at Dillenger so could not have killed Dillenger."
"Public Enemies" doesn't show Purvis shooting John Dillinger. You may be thinking of John Milius' 1973 movie. "Public Enemies" shows Dillinger's death with a commendable degree of accuracy.
"no order was ever given to round up the families nor were they arrested" Not su

He probably liked the royalty-cheques and keeping his real opinion to himself may have been part of the deal.

The book is great. Burrough liked the movie. That is all.