Ambassador At Large has added it up and determined that over half the current members of the UN Security Council have active wars or ethno/sectarian secessionist movements within their territory. New members Bosnia, Lebanon and Nigeria tipped the balance, joining Turkey with its Kurdish problem, Mexico with its drug cartel war, Uganda with its war with the Lord's Resistance Army, China with Xinjiang/Tibet, and Russia with Chechnya.
Technically the UK has sovereignty disputes too (Northern Ireland, Falklands), though neither is currently extracting a high death toll, so this list could be higher than it is. Not to exclude any nation from Council membership, but one should probably have one own's house in order before joining. Eg. Because Lebanon's Hezbollah militia has ties to Iran, that country cannot take any action for or against on the question of Iran sanctions. A country like Lebanon has enough issues without the added geopolitical stresses of being on the Council.