As far as I'm concerned, this is really the first Fourth of July special, since the previous special was just an extra big comic with the Yellow Demon. Hardly something worthy of an Independence Day celebration.
Anyway, in this comic there are a number of things to notice, starting with Roll's very good point. Where do these people live? I don't think the question is really ever answered in the games, though I think I read somewhere that they live in Monster City or something. I think most people just assume it's Tokyo or some futuristic version of some other city of significant size. And if they do live in Tokyo, or some other city in Japan, why would they be celebrating the Fourth of July? After all, to people outside the United States, the day doesn't really have any special significance, does it? I excuse my ignorance by noting that like many Americans, I wasn't really that aware of the world beyond the American border.
Dr. Light's barbeque grill is from Turbo Man's level in Megaman 7. And I hope you noticed the recurring theme of Mega Man vomiting in these specials. It all started with my birthday, and I just can't help but love a running gag like that.
One more note about this comic, and that concerns the drum of TNT the Author is holding. You might recongize it as the same basic sprite that holds Industrial-Strength Ice Cream and the trash can Mega Man's barfing into. The sprite started as an E-soda can (which some of the characters drink when they're not drinking Wily Beer), which was then enlarged and slightly modified. I actually did that only once, and since then, whenever I need a big drum, I just recolor that drum.