Have a similar issue round here, near a large park so plenty of dog walkers about.
There is one dog in particular though who is either Houdini reincarnated or the owners just let it out to roam, though the latter would surprise me as it's an expensive looking dog. It's done its business on my front lawn a fair few times but I have no idea who owns it as I only ever see it out on its own and the dog wardens are never interested when I've rung them about dogs on the loose (including this one).
It's a large aggressive looking dog too so no way I'd get close enough to see if it has any collar disc with owner information. Had to wait for it to move away once before I could get to my front door :(
I am sick of trying to avoid stepping in anything, especially when it's dark, really wish they would have more wardens or something out around here as it seems many people round here just don't care about where their dogs does their business.
I'm not sure I'd be brave enough to front anyone though, save a meaningful glare and hope it guilt tripped them.