I assume you're talking about the chancellor - not president? Germany does also have a president - but he doesn't have a lot of political power.
Both in west-Germany and in today's united Germany, you have to have German citizenship to be electable as chancellor. So even migrants who later became citizens were/are able to become chancellor (president as well, btw).
To my knowledge nobody who wasn't a natural-born-citizen ever even wanted to become German chancellor - but as I said, even if they wanted to 'run for Chancellor' - it wouldn't be a problem - they're allowed to.
Another thing that Americans usually get wrong, is thinking that the German people actually elect the chancellor, which is false. The people elect a parliament, which in return elects the chancellor. Meaning: you have to vote for a party, and the party nominates their candidate. (Obviously this isn't some surprise-candidate. Everybody knows who each party wants to nominate as chancellor)
This is a layer of 'protection', since you don't necessary have the 'winner' of the election automatically becoming the new chancellor. The parliament could compromise on another candidate, if the majority of them feels like somebody would be too 'Hitlery' to elect as chancellor.
But to answer your actual question: Yes, if Germany had a law restricting only 'natural-born-citizens' to become chancellor, then Hitler wouldn't have been able to become chancellor (He was Austrian, be he applied for German citizenship) - and yes, technically, HitlerJr could use the same method to become chancellor today (of course there are several other improvements to the German constitution, that fixes a lot of the loopholes that Hitler used to become more powerful than a chancellor was allowed to.)
So, is this a major mistake and should be fixed? no.
2 points:
1st: in the end, what does it matter if you were born in a country or not? Are people who aren't born in a country more prone to be "evil"? no.
Hitler saw himself as a German. Germany was more of an idea, just like the US is more of an idea than a country restricted by borders. Especially back then, when Germany was still relatively new and a lot of people still wanted Germany and Austria to merge. Same goes for the united states. If .....John Oliver wants to run for president - it's primarily because he feels like an american, and he wants to do good for his country. And in the end - if 51% of the population feels the same, what does it matter where he was born?
which leads me to my 2nd point: laws are just words on a paper. they don't mean anything if there isn't anybody to enforce and uphold them. Laws don't keep countries intact - people are. So if everybody in the US wants to elect Justin Bieber to president, then why shouldn't he become the president? If all Americans think Christianity should become the mandatory religion for everybody, then ...why not?!
Of course, I intentionally chose dumb examples, but fact is: the laws of a country works for the people. And people change over time. At some point it was alright to have slaves, at some point women were inferior to men by law......but these opinions change. But if you don't update your laws accordingly, you'll just create an unhappy population