Is stacking material under an I-Beam to make it level structurally sound and passing code?
These are metal shims - very very common.

You install ibeam and either right after install or after joists are installed you want to level everything out.   You will need to shim at least one side.   

This is really common.   Dealing with ground settling, concrete shrinking and so on over a 60' or longer stretch you have two options:


Pay a ton of money to make sure all the planets align and your beam is perfectly level on concrete cut-outs.  (and after all that money, it could still be off)
Put $2 worth of metal plates under to shim.   


Those plates are not going anywhere - the weight of your house is on them.   As an inspector it would not concern me in the least.   

The only fear you should have is an overzealous inspector in your town - but this should be the same guy that signed off on the house in the first place.   They could require the plates welded to the ibeam or to get a welded piece on that.   This would require a temp post, jack it up and weld it on.   

Also not sure what it looks like if you go further but I like my ibeam resting on a steel flange.   I don't see that here and that bothers me more than anything.  And looking at the picture further I would like to see the top of the beam - really doesn't make sense on what is going on there.

Notes based on 2nd picture:  


Some cities may have a max height of the shims.  I have seen 4" more than once.   I don't believe there are any code standards on this.
The height may not meet code but the most concerning thing is that the plates are not stacked appropriately.   The fact is there may be a lateral force due to this.   Probably negated by the extreme downward force.
And of course they are not welded or tied to the ibeam
How concerned would I be as a home owner maybe a 3 out of 10.   I mean it wasn't done perfect but it isn't going anywhere.   Just the fact that they used this many shims shows they took time to make sure your floors were flat and level.   
The verdict... I don't think it will pass inspection.   I think inspector makes them weld a solid piece to ibeam or steel piece plus 1-3 shims.   I would give this maybe a 10-20% chance of making it.   The good news it is a relatively fast fix and will only cost builder a few hundred.