THIS IS LARGER, SO EASIER TO READ, RIGHT?
Font size alone I agree with you (and a light - serif - white text on a black background has some issues with artifacts, which are visible on the flier), but the whole thing is a mess.
> In the poster on the right, my eye is drawn to the enormous headings, which contain no useful information by themselves.
Yes, it contains. It's an aid to point you to the right section.
Because you scan the bigger text first, the first thing most people will read is "Aikido - Beginner classes" then follow the right column
> The "Come Visit" heading isn't close enough to the address
I agree, this is debatable, one possibility would be to replace it with "Try it" and/or put "Come Visit" or "Visit Us" above the address
> and the address/phone/URL has been squeezed into a single block of tiny, fuzzy text
This is another heuristical cue and to separate it from the rest of the text.