Built a shelf out of 2x4s but some braces do not meet, will they hold?
I paid someone else to build this basic shelf for me because i'm no carpenter, 


Unfortunately, I am afraid the person that built this isn't either.  

There is a major weak point - the screws into the end grain of the cross pieces could just tear out of the wood.  The gaps are not really the problem.  

There are a lot of stronger options for the joint but most of them would involve starting from scratch, which would probably be best.  

If you want to salvage this, you might find a bracket that makes it strong enough.  I don't think it's ideal but the Simpson FBFZ for example might work: