How to escalate a complaint about errors produced by a journal from the Nature publishing group when Editor doesn't respond
As authors we are very frustrated to see our work being distorted online (in front of the readership) 


Release a technical report which doesn't contain these mistakes and explain in the report that the errors were made by the publishing team. 


  we don't know how to...get the errors fixed. 


It seems you have exhausted the usual, informal routes. Perhaps you can escalate with your university's legal team, since there's surely a breach of contract which reflects badly upon the university. A strongly worded legal letter will hopefully prompt action.