Well I can tell you about the Pig War...because it happened near where I have lived for most of my life, in Washington State!
When the US-Canada border was established along the 49th parallel in 1846, the maps for the Strait of Juan de Fuca and the Strait of Georgia, between Washinton and British Columbia, were not yet accurate. So by 1859 parts of the San Juan Islands were questionable still, and the pesky pig somehow crossed into No Man's Land and was eating the potatoes, so the farmer shot it!
Soon things escalated into a face-off with about 500 Americans with some cannon and five British warships with more cannon. They hurled insults to try to goad each other into firing, because both sides had orders not to shoot until the other side fired first...but discipline held and nobody started shooting.
So they ended up with joint military occupation of the San Juans for a while, with an interesting situation that persists until even today (according to Wikipedia), where 'the Union Jack still flies above the "English Camp", being raised and lowered daily by U.S. park rangers, making it one of the few places without diplomatic status where U.S. government employees regularly hoist the flag of another country.'
Here is a current photo of English Camp on San Juan Island, with the Union Jack still flying there!