Should Contractors be responsible for safety of constructions being implemented, if Designs were created by another party, and they contain mistakes?

Yes, I think the contractor should be responsible... it is your job to make sure some one else has done their work correct ... you need to make the designers to correct there mistakes from the start of the project ....... therefore you cover yourself  

Mr. Sardar Mardookhy made a good point

I agree with Mr. Sardar Mardookhy answer.

If contractor A has a Contractor B for its construction design,... surely the responsibility is by contractor A,

But if contractors B & C are working for A company for design and construction, considering safety in design and implementation would be under their responsibility individually.It means if implementation is done exactly according to design the mistakes are under design responsibility.

There are a few propositions coming into the picture. If before the implementation, the contractors were aware of the issues with the design, they should have put that to review immediately with counterparts from the other party. However, if the contractors have ignored that, then they might be held responsible partially, and not fully, because the contractors were never involved in the design. 

However, if it was given for only implementation of safety and construction by the other party to the contractors, the contractors can be in no way held responsible , because in this case, it was the responsibility of the other party to review and close the deficiencies in design before giving it to the contractors for implementation. In this scenario, it might also happen that the contractors do not know anything about design, and in no way they can be held responsible.

Design sometimes had mistakes and this is were the contractor's must make sure that everything are to the exact standard before they will commence a certain project, usually an experience and well oriented contractors will request the clients for a certain period of time to thoroughly review the design.A contractors job is not only to implement the project but to make sure that everything are in accordance to standard construction practices which are but not limited to, the correct design and specification, the safety of its worker, the proper storage and protection of the materials, and so much more.

I agree with Gourab Mitra^^^^^^^^^^^^^^^^^^^^^^^^

No, they shouldn't , they should be responsible for implementation mistakes only , if the project was issued as design and implementation , the answer will be Yes,  they responsible.  

All rights and duties related to contractor and owner are written in a contract , this contract is presenting by law experts whom working in the owner company which contains, in addition to above, all specifications of the work and duration of the implementation and the costs as well as the pay method and the consequences of a delay or lag in executing .

 Dear Sir,

I believe there must me safety officer in any company/subcontractor he should verify first the drawing /designs and if any redrawing   he have to mark and give proper explanation for the correction.  

yes he should be . so he  have to use high  experience Engineers  to study the designs prior to implementation (alpha testing )  and follow-up implementation properly at every stage

Almost of the contracts, and construction norms, assign the construction safety to the contractor as he is the professional and it is a part of his liability. The contractor has to review the design as a part of his offer and the project is in his possession during the construction time and he owns all the tools, technique and experience to catch design mistakes, suggest and implement solutions.

From day one of the project.  Safety is the main thing which we need to consider, normally all are responsible for an safety issue, suppose client & consultant will be consider as a contractor A, execution party will be  contractor B, B may engage N number of X,Y,Z contractor, but  considering a safety norms from  Z to A, upto to client  and owner of  the company are responsible, as its a very sensitive issue every one need to follow the norms, A need to monitor B, B need to monitor C,