As with all borders which happen to be in a place where people are, if there is a legal question, specialist will look at where the person was when the incident happened.
If you have a health insurance which is only valid in the US, get a travel insurance that covers medical care (mostly emergencies only) when in Canada, so that if a series of accidents places you on Canadian ground before the final accident, you are covered.
In case of accidents where the exact location of the persons or their belongings are important, you should take a full set of photos all around, making sure you include visible border markings where important.
In daily life, the border will make little difference, because the people living in the area are aware of it and are ready with insurances and such.
It are the tourists who come to these border crossing areas, like to do shopping across the border, who might be confused and might even get in trouble.
As long as the border stays friendly, there will be few problems.
Berlin, after it was divided after the war and more so when the wall was build, is an example that a place does not need to be on a national border for difficult situation to come in existence. (In that case, a 'no man's land' was created between the people living near.)