“vulgar scandal stamp'd upon my brow”
'Vulgar' here means 'common' or 'belonging to the common people,' not obscene as in modern usage. 'Scandal stamp'd upon my brow' continues the conceit of line 1: public censure is a mark pressed into him like a seal into wax, and the beloved's love now fills that impression.
“o'er-green my bad, my good allow”
'O'er-green' means to cover over with fresh green growth, the way grass or moss reclaims a scar in the earth. 'Allow' here is stronger than modern 'permit': it means 'approve' or 'sanction.' The poet says that as long as the beloved covers his faults and endorses his good qualities, no other judge matters.
“None else to me, nor I to none alive, / That my steel'd sense or changes right or wrong”
'Steel'd sense' means a judgment or perception hardened like steel -- made firm and impervious. 'Or...or' is an archaic correlative meaning 'either...or.' The poet declares that no other living person can shift his sense of what is right or wrong: that power belongs to the beloved alone.
- TLN 1565biblical allusion
“my adder's sense / To critic and to flatterer stopped are”
The adder was believed to make itself deaf by pressing one ear to the ground and stopping the other with its tail, so no snake-charmer could reach it. The image comes from Psalm 58. The poet says he has made himself equally deaf to both critics and flatterers -- neither hostile nor flattering external judgment can penetrate him, because only the beloved's voice counts.