I have a few ideas other than Greece-Turkey, although they are probably at least borderline-ASB:
One is to somehow have some sort of rabid, ultranationalist party win a general election in Spain after Franco dies, and this government for revanchist reasons or to distract the population from domestic turmoil, makes an attempt against Gibraltar in a move reminiscent of the Falklands War.
Another has to do with the International Court of Justice in the Hague. As one may recall, conservative Republicans in Congress were up in arms over this, refusing to permit the treaty to be ratified, while claiming it was an affront to American sovereignty and would be used by 'leftists & anti-Americans' to prosecute American soldiers and officials on "trumped-up politically motivated charges of war crimes, waging aggressive war" & other stuff along those lines. One even went so far as to submit a bill, which if passed & enacted into law, would have required the president to order an operation to rescue any Americans held in custody for trial there by military force. Now if this bill did pass, some American did end up awaiting trial in the Hague (whether or not the charges were legitimate is irrelevant), and a US president willing to order such a mission carried out by the US military which obeys those orders (probably need some sort of rabid neocon ultranationalist imperialist farther out there than the likes of Cheney, Wolfowitz (sp?) & Rumsfeld), then cue a massive shitstorm, particularly if supporting assets make a big mess (i.e. lots of collateral damage).
A third possibility involves the Cod War turning hot- have some hotheaded British destroyer or frigate captain interpret a bumping incident as a deliberate ramming attack by an Icelandic vessel or a boarding of a British fishing vessel as an act of piracy, to which the British captain responds by firing on the Icelanic vessel, and you could have a bit of a war until the US & the rest of NATO step in to restore sanity.
A fourth involves a dispute between Canada and Spain over who could fish where in the 1990s that led to several Spanish trawlers being seized, and hotheads on both sides talked about sending warships to enforce their claims- have a Canadian and Spanish warship get into a shooting incident over a fishing boat, and a war could start that way.
A fifth involves something I've seen on threads about Quebec secession- there's been some discussion about the French intervening in favor of Quebec in such a scenario, especially under DeGaulle. Now this is a stretch, but if the French do attempt such an intervention, neither Canada nor the US are likely to be very happy at that turn of events. It's even more of a stretch, but this could cause a war if say a US CVBG was sent to intercept the French and mak them turn back, the French refused, and things escalated into a shooting incident, or Canadian troops saw French personnel on Canadian soil as hostile invaders and reacting accordingly.
You could also have the US get really pissed off about the Israeli attack on the USS Liberty and decide to retaliate by bombing a number of Israeli air and naval bases.
There's also the possibility of Argentina having another go at the Falklands, although that should probably go into future history.
However, of all these, the only two that don't seem rather implausible without being preceded by massive butterflies to me are the last two, and really, the best ways to have first-world democracies going to war against each other tend to involve pre-WW2 PODs, such as something leading to any combination of the US/Britain/France going at it.
Perhaps if WW2 ended with no UN and no ongoing Soviet (or Nazi) threat resulting in a prolonged Cold War to force fundamental strategic interests of first world countries into alignment and into an alliance, these would be more plausible ways to start a war, as wars have started over stuff like that in the past.