There is plenty of information out there. Try googling Operation Soberania Beagle Conflict. Better still try 'Operación soberania' or 'el conflicto del Beagle' as, unsurprisingly, you will get much better hits in Spanish.
for example:
tps://aquellasarmasdeguerra.wordpress.com/2013/01/23/algunas-armas-utilizadas-durante-el-conflicto-del-beagle-la-guerra-que-no-fue-1978/
w.taringa.net/posts/info/14696583/El-Conflicto-del-Beagle-Argentina---Chile.html.
There's even a very good Chilean feature film on the subject Mi mejor enemigo whih is viewable on youtube in it's entirety ( not sure if the subtitled version is available)
In short, the Argentine Junta refused to recognise the 1977 arbitral decision over the long running Beagle Channel dispute. The two countries had exchanged fire back in the 1950s over the issue.
Argentina prepared to invade Chile, taking the islands in the Beagle Channel as well as launching major offensives across the Andes, with the aim of knocking out the Chilean fleet and capturing the key cities, including the capital, Santiago.
Mad as that sounds it came within an ace of happening. The troops were mobilised, the Argentine invasion fleet set sail and the whole thing was averted only after a major storm delayed the naval taskforce. That gave just enough time for papal intervention to get the whole thing called off. Just as well for Argentina as the Chileans had good inteligencel and had deployed their fleet and troops to meet any threat and had even dynamited some of the smaller passes through the Andes as a precautionary measure. A former Argentine COS was interviewed a few years ago and conceded that they would likely have been beaten had the ear broken out.
Where it has the prospect to become a continental conflict is the friction, still evident to this day, albeit at a much lower level, between Chile and Bolivia and Chile and Peru. 1978 was the 100th anniversary of the War of the Pacific where Chile had taken large chunks of Peruvian territory and Bolivia's access to the sea. Pinochet even ordered that the celebrations for the centenary were to be low key for fear of stirring up a potential second front. Tensions were high around the time anyway. Chilean diplomats were expelled for alleged 'spying' in Peru.
Chile had a number of contingency plans for various war scenarios, including their nightmare scenario, war against Argentina, Peru and Bolivia at the same time. There is evidence to suggest that this plan, HV 3, was the one that Chile initiated in December 1978, at least the mobilisation aspects. Peru at this time had a pretty capable force and the best MBTs on the continent in the form of T-55s.
Argentina had it's own, albeit less realistic problems. It devoted an entire corps to securing the border with Brazil to forestall any potential Brazilian moves. Brazil actually did mobilise it's forces along the border but in reaction to Argentine mobilisation. None of Argentina's neighbours really fancied an aggressive Argentina flushed with victory. This is the time period when Brazil was actively developing it's own atomic weapons program, with Argentina as the principle target of deterrence. It's not entirely beyond the realms of possibility that Brazil could have been drawn into a wider conflict.
Peruvian intervention might have had it's own ramifications. Peru was a fairly aggressive and expansionist state in the mid 20th C. It had fought an unsuccessful little war against Colombia in the 1930s and a successful one against Ecuador in 1941. That war robbed Ecuador of huge tracts of territory and was a sore that would fester for years, Ecuador and Peru fighting again in the 1990s. Ecuador was fairly flush with cash in the seventies as result of the oil boom there and possessed a relatively modern air force. It's possible that with Peru engaged on its southern frontier, Ecuador may have taken the opportunity to retake its lost territories.
So, with just a little stretching of the actual historical narrative you can easily see a big war or series of wars breaking out.