Everything you listed are good points using theoretical, book knowledge, but isn't the only "objective" way to evaluate the two posters to put them in front of a sample of the target audience and measure their reaction? What you're doing is applying general guidelines as if you can determine the overall quality of a design by running the design through a checklist.
For example, you dock the left for having indistinct headers with inadequate contrast. But that's actually a good thing, since the headers are useless in both posters! But only in the right example are they distracting because they followed the "good design checklist".
The headers in the "after" picture aren't useless. They communicate:
* Aikido
* Beginner
* Regular schedule
* Come visit
That seems like a very sane set of goals for a poster about an aikido class.
In the "before" version, the copy about the "mind, body, spirit" connection of Aikido is set in a larger font than the text saying people should come visit!
Who, what, where, & when are mandatory items on a checklist for this type of communication. But if the way you point to them draws attention to your finger and away from the vital information itself, you've failed. That's why the headings are useless. You allude to this yourself in your final sentence.
For example, you dock the left for having indistinct headers with inadequate contrast. But that's actually a good thing, since the headers are useless in both posters! But only in the right example are they distracting because they followed the "good design checklist".