First, as I have stated frequently, the location should have been chosen for its sound - or lack of it - as much as for its visual aspects.
Once the director and producer have made their decision regarding the location, the production sound mixer has no choice but to deal it. If there is constant traffic there is not much the PSM can do about it. There are always going to be extraneous sounds when using real locations. The PSM will wait until the set is as quiet as it can get to call "speed", but you surely don't expect the PSM to cut the take just because there was the beep of someone unlocking their car down the street?
Directors and producers generally don't have much patience with anyone who interferes with their shooting schedule. Is the entire production going to wait for an hour while the landscapers do their job? How many low/no/micro budget projects have the budget to "bribe" a cleaning crew to postpone their office cleaning for several hours? It is the job of the director and producer to mitigate these problems as much as they can. This is part of what preproducing for sound is all about, finding out when landscapers, cleaning crews, motorcycle clubs, parades, skeet shooting contests, etc. are happening near their chosen location.
Now, as to individual sonic events like sirens, an obvious crew noise (i.e. a sneeze), wind hits and the like, yes, the PSM should notify the 1st AD, and notes should made on the sound log. But if the PSM is also the boom-op, as is the case on most low/no/micro budget projects, then the job of being the boom-op takes priority; his/her job is to capture the dialog. Most low/no/micro budget directors and producers don't even want to wait while while the PSM/boom-op maintains the audio log in the first place, much less take the extra time to note every extraneous noise.
And another point; the director and producer opted not to pay a fully professional sound crew, so they will have to deal with the shortcomings of sound folks who are probably learning their job just like the rest of the crew - and most probably the director as well. You get what you pay for.