Valda, in your first 2 senteces the following meaning is used:

aside - used after nouns to say that except for one thing, something is true (Money worries aside, things are going well - У нас всё нормально кроме финансового вопроса"... - notice i ve used the word кроме here.

So to elaborate on the two of your sentences, i think this meaning is used here:
"That aside, I would say it's an interesting concept." - Не взирая на это, данная идея представляется мне интересной. (i am using не взирая на это here)
"Legal aspect aside, you must support your brother." - Несмотря на юридическую сторону дела, ты должен поддержать своего брата. (несмотря на - i am using it here)

Now in your 3rd sentence
"Let's put it aside for a moment and concentrate" - the meaning of ASIDE is absolutely DIFFERENT!!!

like some folks above wrote - here it means В СТОРОНУ - but ONLY! in this one of the three sentences...(this means here moving to one side, out of the way physically or figuratively)

So "Let's put it aside for a moment and concentrate" - Давайте отложим этот вопрос на время и сосредоточимся. or Давайте на время отложим этот вопрос в сторону и сосредоточимся... - Notice i am even not using В СТОРОНУ in one of the variants.