The qualification is still unknown, hard to speculate other than all 3 marines seem to be physically quite powerful. If the logia admiral theory goes through it won't be a qualification, but rather logia users tend to be considerably more powerful than other fruit users. Their elements also have less weaknesses or mortal enemies so it would be a lot harder for an admiral to be taken out, given only one person could be their enemy by coincidence, the odds are not in favor of them losing, so in a way, having 3 admirals as logia users may even make them the strongest admirals ever in the marines.
Does this make Sengoku weak? Of course not. During the meeting between Whitebeard and Shanks, Whitebeard does mention Garp and Sengoku's name while reminiscing about the supposed 'old days' on the sea. If Sengoku wasn't that strong, or at least didn't have a reputation, why would one of the strongest pirates of the past and present mention his name along side Garp and Roger himself? Obviously Sengoku had quite a reputation, he must've been a pretty tough opponent too. While age might have caught up with him, it's possible that Sengoku still has a bit of strength left in him.
