If you have designed something, structure or element thereof, you are interested in whether or not the fabricator clearly understood your intentions with regard to element size, material, connections, welds and weld sizes, coating, number required and so on. You are also interested in the fit of those elements with others. No one knows teh design better than you and it is an opportunity to discuss with the fabricator how it is to be fitted together so that problems during erection may be minimal.
The AISC's "Code of Standard Practice for Steel Buildings and Bridges" covers the responsibilities of the owner's representative and the fabricator with respect to shop drawings.
In general, the checker should verify that the shop drawings conform to the contract documents. That includes to verify the member sizes, the general arrangement of the framing, how the members are connected, etc. Although the length of the members, drilling for bolted connections, cuts, and others shop details are not the resposibility of the checker, it is a good practice to check at least a few of those dimensions and details to get confidence in the detailer's work.
Also the checker has to review the connection details if the connections were not detailed in the design drawings.
Number and capacity of bolts and welds, size of gusset plates and clip angles, cuts in the members, and any other details that affect the strenght of the connection should be verified.
