There have already been many justified critical comments on the Saudi execution of a Shia cleric. Here I will not add much. Together with the severing of diplomatic relations with Iran it seems to be a deliberate irresponsible act of the same sort as those carried out by Turkey. Sacrificing internal coherence for other purposes. For Erdogan strengthening personal power. For the Saudis sabotaging Iran's integration into int'l politics.
The execution is morally wrong, and on the political level stupid. Anti-Iranian hawks in the West could have used the Iranian rocket program and the provocation by the Revolutionary Guard in the Golf to disrupt Iran's integration. But the Saudi action rightfully turns attention to the semi-barbaric nature of the leading circles in Saudi Arabia.
The adverse effects on the efforts to reach a political settlement in Syria and the fight against ISIS are obvious. But seen in Riyadh as of less relevance or even desired.
The rising ethnic tensions in Saudi Arabia already fueled by the intervention in Yemen will worsen still more. As with the result of the new oppression of the Kurds in Turkey the saudi kingdom faces ethnic tension and conflict. Whether this is a result of political decline as in Turkey or just political immaturity is not clear. It is probably both. It would seem less likely that Sheik Yamani as minister would have sanctioned such policies.
As said in other posts (see Ethnic Cleansing in the Arab World) during the last century the distributed patchwork-nations of the Oriental civilization have been and still are being transformed into Western type territorial nations with a wish for coherent territories. This process often involves ethnic cleansings.
Generalized to the wider Middle Eastern context the execution of the cleric and the resulting conflict with Iran and Shias elsewhere could contribute to the start of a new round of ethnic conflict and cleansing in the Middle East. This time between Shias and Wahhabis or worse Sunnis in general. There have already been attacks on Sunnis in Iraq and new tensions between Sunnis and Shias in Bahrain following the execution. We don't need Sunni-Shia conflicts aggravating and spreading to more countries. And we certainly do not need ethnic cleansing and streams of refugees in an area from Iraq to Yemen. The Middle East has problems enough already!