Contractor cut joist hangers to make them fit
No, it’s not acceptable to cut the joist hangers.

In order to determine if they are acceptable anyway, there are several issues to review: 1) hangers are notched, 2) incomplete nailing, 3) wrong nails, 4) wrong install of fasteners (angled install in lieu of perpendicular to joist installation).

1) Notching the hangers voids the allowable stresses published by the manufacturer for each hanger. However, if the hanger is not stressed to its maximum allowed, the engineer can review and determine if it meets the “intent”. 

2) 3) and 4) Published allowable stress values are determined by installing the hanger in the proper manner, as per the manufacturer’s installation instructions. When the fasteners are not correct, missing or improperly installed, then the designer will need to make a determination that they meet the required design loads. 

If you have a Building Permit, I’m sure the Building Official will want the designer to provide “certification” that the installation is acceptable. If it’s not acceptable, it will need to be re-done. 

So, if the correct wood ledger was used and it’s impossible to comply with the drawings, the engineer will need to redesign...and pay to have it done correctly. You can see that the engineer will do everything possible to accept the lack of nailing fully into the ledger/beam...but will probably want the hanger replaced (at the contractor’s expense). 

It’s important to you to get this corrected or have the engineer provide the certification, because if there’s a problem in the future, they’ll both point the finger at each other and you’ll be in court forever.