Are there any differences between the "German" language in Hitler's days and the "German" language today. I mean in terms of spelling, grammar, definition/meaning, etc.
From 1889, when Hitler was born, until now (2016), there have been writing reforms for the German language in 1901, 1944 and 1996. The reform of 1996 was adjusted in 2004, 2006 and 2011. But these all were just changes in how to write words, i.e. orthography. None of these reforms did really change the language itself, i.e. the way how people speak with each other. No meaning of words and no grammar rules were changed by these reforms. No new words were invented, no words were deleted, and the meaning of words was not changed by these reforms.
Hitler lived from 1889 to 1945, this is between 71 and 127 years ago (counted from 2016). So, we are talking about a time difference of about one century. I guess the differences are similar to the differences in English or any other language within the period of one century.
Today we have tons of words that did not exist 100 years ago. This are new words like internet, skateboard and car-sharing, but also words like television and even blitzkrieg (which was invented by the Nazis, so it didn't exist when Hitler was a young boy).
We also no longer use certain words that were common a hundred years ago. Sorry, I don't have examples for this, but just watch historic movies and listen to what people are saying there.
And of course the meaning of some words has changed. Changes in grammar can also be found in almost every living language, and German is a living language, so it is permanently changing.
Considering spelling, there was a reform in 1996:
in the course of which several changes were introduced. (e.g. doubled consonants, when preceding vowel is pronounced short. Removal of a lot of "ß" and replacement with "ss". The aim was to unify spelling more strongly)
Regarding "definition/meaning", the first thing coming to my mind is the term "Propaganda" which, at the time, was afaik a common word for "political advertising". "Propaganda" nowadays has a strong negative connotation.