Today Saudi Arabia executed 47 individuals, 46 of whom appear to be Sunni (there are rumors that 3 of them were Shi'a) and allegedly linked to Al Qaeda, and one, a prominent Shi'a cleric. Iran, as the self-proclaimed protectors of Shi'ism and Shi'ites has expressed its discontent in a variety of ways; Iranians protesting at the Saudi consulate in Mashhad who seem to have caused a fire, and a large demonstration is expected at the Saudi embassy in Tehran tomorrow (there are now breaking reports that the Saudi embassy in Tehran has been at least partially burned as well from molotov cocktails).
The inclusion of Nimr in with the 46 accused terrorists/political prisoners is interesting as his case has been very high profile. Rumors of his impending execution in the past few months outraged Iranian officials and the general public. Even the relatively quietist Marja Ali Sistani, based in Najaf, Iraq, involved himself by writing to Saudi officials asking for Nimr to be pardoned.
Signs of attempts at rapprochement between Saudi and Iran appeared throughout the first years of Rouhani's administration, despite ongoing proxy conflicts in Syria and Yemen as well as Iraq to a lesser extent. They have not been exclusively positive statements, as Hashemi Rafsanjani, one of the more pragmatic Iranian political figures, has also strongly condemned Saudi actions in Yemen.
Despite Iran's own status as a major human rights abuser, despite its disproportionate use of capital punishment, and despite its lack of due process and an independent judiciary, the Iranian government is objecting to another state's use of this tactic. This is an opportune time however, as Saudi is stuck in the quagmire of Yemen while Iran appears to be at least nominally withdrawing from its own in Syria, as Russia takes the lead there. Nationalism and sectarianism are important, and I expect Iran to exploit this while heavily criticizing Saudi Arabia's human rights abuses (and ignoring their own).
If it is true that there are additional hundreds of Saudi Arabian executions pending, and especially if any of the individuals sentenced to death are Shi'ite, there may be further diplomatic tension between the two states. I am less familiar with Saudi politics, but this would appear to be some sort of statement from the interior ministry, or from the new king as to what their approach to other religions and to local international politics will be. An embrace of hardline ideologies at an increasingly volatile time in the region is worrisome.
Because the reports of the attack on the Saudi embassy are true I expect there to be significant diplomatic problems, though I am not sure either side is eager to engage in full-on conflict. The UK embassy was stormed and damaged a few years ago, but there is not the same level of animosity (or proximity) involved. Saudi Arabia will probably expel the Iranian ambassador (he already was summoned over "hostile remarks" earlier today), and potentially file complaints with the UN. If Saudi Arabians attack the Iranian embassy in Riyadh or consulate in Jeddah, a response from the IRGC-N in the Gulf is not out of the question.
If things spiral out of control, I expect this is how it would happen. For now, until we see what happens in Saudi Arabia it doesn't seem that things will be too bad. The more damage done to Saudi facilities in Iran, the worse it could get.
UPDATE #1 (1/3/16): KSA did end up expelling diplomatic staff, and additionally withdrew its own staff and broke ties with Iran. They broke ties in 1988 before restoring them in 1991. Iran has the initiative now. It remains to be seen if they will retaliate through their militant proxies in Lebanon, Syria, Bahrain, Saudi or Yemen, or with the IRGC Navy. They could also give the green light for Hezbollah to attack in a Central Asian or North African country. At this point I don't think they would do this outside the region.
