Perhaps the S is in the wrong place>> Some governmentS have.... Solves the problem! I think it was a typo/mistake.

I agree teacher Moira 's explanation. it is the typo that makes that student be loss at the whole sentence. The original is : Some government shave forbidden cigarette commercials and launched anti-smoking campaigns. The typo occurs at the word "shave", the "s" here should be positioned after the "government" so the original is : Some governments have forbidden cigarette commercials and launched anti-smoking campaigns. = Some governments have forbidden cigarette commercials and (some governments have) launched anti-smoking campaigns. its Chinese version is : 一些政府已经了禁止香烟广告，（这些政府而且已经）发起了反吸烟运动。 Note: The "Some governments have" is omitted before the past participle "launched" for the sake of the concise form of the original because of the conjunction "and". (说明: 由于连词"and" ，为了保持原文的简洁形式，过去分词"launched"前面省略了"Some governments have" ）

Definitely a typo. It's some governments have ... 100%

Yeah, I think it is a typo since moving the "s" makes the sentence so perfect. And about your question as to whether it should be "have" or "had", "have" is the right one. The structure is like "governments have forbidden ... and (have) launched ...", meaning "have" applies to both "forbidden" and "launched". Such a distributive usage happens all the time over "and" and "or" (and even with other conjunctives too), as in "I have tried and ((I) have) failed", "I could say yes or ((I could) say) no". You could say the full version including every word, or have only the subject omitted, or both the subject and "have/could" omitted. In most cases, we would go with the shortest version. I am not sure but if you're thinking of using "had" because there are two verbs in a sequence and it would be natural to use "had + PP" for the first one and a simple past form for the second, it is a bad idea. You don't need two different tenses for events happening sequentially because it is the natural order we assume (i.e. you wouldn't mention things in reverse unless there is a special reason). Saying "I had had lunch and went out" would just make it more cluttered and harder to understand compared with the more clear and natural "I had lunch and went out".

That sentence has bad grammar. You are right that it looks odd using launched (past) after using shave (not past). They need to fix their grammar. Still, I can guess they are saying: a government, or some governments, have shaved, or will shave, or tend to shave... And by shave they mean cut / drop / kill / axe / remove / end / terminate / reject / discard. They are not shaving hair off their body, but they are shaving (cutting) commercials from their schedule. So the word is valid here, but it's a rare metaphoric slang usage of the word, hence why it doesn't appear in every dictionary. But better dictionaries should say this word can sometimes be used more generically without necessarily shaving hair.