That movie influenced the audience badly.

I don't think that 'badly' necessarily means something negative. Maybe, depending on its context, it could be 'influence strongly', right?

So if the sentence was 'That movie had a bad influence on the audience,' could it be also ambiguous between 'a strong influence' and 'a serious influence'?
Hi, Taka!

Yes, you're right, "badly" can mean "very much": "I badly need those painkillers". But maybe here the ambiguity may be created by the verb "influence". We instinctively expect to hear of a good or bad influence, not of a strong one, so our minds may tend to understand "badly" as "in a bad way".
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Hi guys,

I feel that if you look at

I badly need those painkillers or I badly need to see her

there is still at least a hint of negative feeling. My need for painkillers is a bad thing. Even, I suggest, the strength of my need to see her is a bad thing in a way.

To me, that movie had a bad influence on the audience definitely suggests a negative outcome.

Interestingly, I believe current teenage slang is, if you think something is very, very good, to say 'That's bad!' It's a use of opposites.

Best wishes, Clive
(Clive, I can tell you my need for painkillers right now isn't a bad thing!)