Seems like this would produce some naturally bad incentives. My guess is you would see both sides work the system in concert in a way that protects the 'core' members of both. If there are incentives to 'bust' members of the other team, they could always just hire patsies specifically to be groomed and sacrificed as an exchange with the other side.

The alternative is two sides fighting a war of escalation which would likely encourage scary corrupt behavior. "Those guys busted Johnny for some minor offense, so lets go get some dirt on one of their guys, or plant it. Can't let them think they can just mess with us"

This is going by the current us vs them mentality of the police forces.

To prevent regulatory capture/tit-for-tat/spontaneous alliances, I would think that we need a loop at least three agencies long; Police A watches Police B who watches Police C who watches Police A. We also need proper incentives for all of them to act appropriately. Otherwise they will be either overzealous or lackadaisical.

Yes, but only if they organize pronto. Recall that direct interference in a nominally lawful police activity is obstruction of justice and itself a prosecutable crime.