After improving my standing with a faction that wasn't previously very hot about me, I keep finding lingering hostile ships, stations and lasertowers. Not only does this hippie sensibilities, but they also often attack my remote ships or deny the trade of valuable resources. How can I convince them to forgive and forget?
Lingering hostile ships can often be dealt with by apologizing and/or scanning (make sure you have a valid police license to scan in that sector). If that fails, make them have an 'accident' with a bigger ship.
Stations have to be hacked by hiring a hacker, who show up as a lightbulb icon (note that the icon may be overridden by another mission type, so make sure to open comms with every station with a mission icon if you are desperate). They can be found on any pirate installation as well as race-controller stations in border systems within 3 jumps of a hostile station, as stations further away cannot be hacked.
Lasertowers are the most annoying. The only way I have found is to destroy them. You can avoid reputation loss by destroying them in as few hits as possible, though you will lose your police license; the best way is to shoot a Hammerhead missile at it, since it will destroy the lasertower in 1 shot. Often, this will cause an attached station to become hostile, so you'll have to rehack them, although contacting the station and requesting docking permission may turn it blue.