MM began being beefed up -- accidentally, I believe -- in the Justice League Detroit days. The creators mistakenly gave him the power to phase up through a building (probably forgot he wasn't the Vision). Ironically, they also downgraded his power-levels in that same run.
Interesting that this run should be mentioned as the point where the Martian Manhunter's power levels were boosted up somehow. Remember that one issue of the Giffen Justice League where the Manhunter actually outwrestles and outfights the Gray Man possessed Superman-equivalent Captain Marvel? Where at any point prior to this was there any indication that the Manhunter could be the equal of Captain Marvel in a brawl? If anything, there are occasions that contradict this assertion.
When was the last time the Martian Manhunter used "Martian Breath?" Of all his powers, this one makes the most sense. After all, Mars's atmosphere is considerably thinner than on earth.
Post Crisis, in The Weird, he was able to use his other powers with his invisibility for the first time. That was the first true difference in Post Crisis continuity.
Interesting. In the retcon series JLA: YEAR ONE, the opening scene with the Martian Manhunter involves him using his Martian Vision as a burst of heat SIMULTANEOUSLY with his invisibility. As if that was the writer's intention to say, "okay, he had these powers since day one, and it wasn't a mistake on the part of the writers."
Ostrander in MM's short-lived series gave him space capability. IIRC, in the JLA at the time, Morrison mistakenly gave him super-speed. Not being space capable nor superfast were necessary shortcomings to explain why J'Onn didn't just say "Huh? This backwater planet? Better hightail it home before dinner!" when he was accidentally teleported here. IOW, he needed those lack of abilities to explain why he was trapped here -- a basic theme of the MM.
This also doesn't jibe with the fact that the JLA jumpshuttles used in Morrison's day were based on a Martian design (for instance, in order to use them appropriately, the Martian Manhunter had to assume a more "Martian" form); why would a race with personal interstellar capacity use jump-ships?
I was never that happy with the MM series a few years back, where it was explained that J'onzz had numerous earth ID's. Even one of a pet cat. This made no sense to me as to why J'onzz would waste such time on such trivial things.
It WAS a rather unique suggestion. I for one, liked Big Doof, the supervillain identity the Manhunter assumed.