In regards to the police are your friends, the only thing i can think of where the police are actually of help, is when we are escaping day 3 of framing frame (non stealth), as you escape using a helicopter that is supposed to blend in with the cops and media choppers.

I bought the full steam trading cards to have a look at the wallpapers provided by each card and here are the things i noticed
Steam Trading Cards Image Analysis:

Bain Card: Bain sitting at his desk with 3 screens, each containing an image from the trailers, on the right we have the bank mission, in the middle seems like day 1 of watch dogs and on the right, it is diamond heist.
What is interesting is the 4th projection, which seems like a projector screen on Bain's wall where he is looking at Crimenet, but with a slight advantage than us, in the bottom right there is a ZOOM LEVEL measurement set at 1.46X, and X,Y Coordinates X548.8 Y381.5.

Zoom Level: 1.46X
Coordinates: X548.8 Y381.5

Torn Page of the guide of Bain Card:
Shows a guard holding a torch and sitting on a chest filled with money, while holding the hand of a peasant carrying a knife, and a man with a flag infront of a castle in the distance, the moon is shining, so it is night time, and one guy with a bag over his back, the paper's corner is burnt.
This to me sounds like day 2 of rats
Burning Paper = Intel Burning
Peasant with knife = The betrayal in the deal
Money Chest = Extra Cash for the extra Meth Maybe
the Moon = night time further proves this but this is all mere speculations.

Hektor/Vlad/Elephant Cards: i think there might be something in their backgrounds, but my brain just fails to realize what might be there if there is something.

Hoxton/Wolf's cards : both are not wearing body armor

Dallas/ Chains' card : both are wearing body armor (the one hidden under the jacket)

There was a post in regards to bain saying that the pool in counterfeit in payday 1 exploded or something like that, and the same pool design if i remember the old pool design exists in the big oil heist.

Big oil has the same pool from Payday 1, where you have to sneak in to get the fusion reactor, it is at the back of the villa, could have something to do with that.