A small war at that time would have been a great boost to Callaghan, as a distraction from the Unions and the economy going down the pan and, as to an extent happened, the restoration of national prestige. (Even Harold Wilson later stated that had he had a "Falklands" of his own he would have been far happier.)
The Argies wouldn't have had the air-launched AM.39 Exocet, merely the older MM38s on their destroyers and the Belgrano. As was shown in OTL, in the face of British SSNs the Argentine surface fleet was a paper tiger, so without air-launched Exocets they might never had chance to use any ASMs - which sank Sheffield and Atlantic Conveyor - against the RN.
As its sole aircraft platform, Ark Royal would have been vulnerable.
Phantoms were old, less manoeuvrable in dogfights than the Sea Harrier and would not have benefit of AIM-9s; moreover, far fewer were carried aboard Ark than Sea Harriers aboard Inv. and Hermes, even if the Ark was deployed "top-heavy" with fighters in lieu of Buccanneers.
In their favour, however, they had Skyflash/Sparrow long-range AAMs, something the Argentinians did not, and still more than a match in aerial combat against Mirage IIIs and Skyhawks.
Aside from carrying dedicated fighters and maritime strike aircraft, the Ark Royal carried Gannet AEW aircraft, something lacking in 1982 and responsible for the loss of several ships.
Even though the majority of the warships in OTL 1982 were for the large part unsuited to dealing with air attacks - being designed as Blue Water ASW units - in the mid-70s there were an awful lot more 1950s/early 1960s frigates etc. in service, lacking modern sensors, and very few capable modern vessels entering service in any appreciable numbers.
Air Defence aboard the ships would have been far more limited, lacking Sea Dart and Seawolf and instead being reliant on 1950s Sea Slug and Sea Cat and - again as OTL - severely lacking any CIWS.
Obviously an important factor if a concentrated formation of Skyhawks etc. carrying iron bombs made to attack the Fleet whilst Mirage IIIs engaged with the Phantoms.
There were also fewer SSNs availabe to the RN in 76/77 than there were in 1982.
Moreover, one of the Argies' modern subs did make (approximate) contact with the Task Force in OTL, but a faulty fire control system let them down. Even so, the RN, arguably the most-experienced ASW force in NATO, could not find it. Had these subs been ship-shape, possibility is they could have loitered off the Falklands and sunk something.