31.3 has 2 different kinds of guys who look at stuff: Inspectors, and Examiners.
Inspectors work for the Owner and can look at pretty much anything they want
Examiners are responsible for the QC functions performed by the mfg or fabricator, and have specific extents of examination per the code, which can and often are significantly modified by the Contract.
There is also a possibility, depending whether or not the alternative to leak testing is/can be performed, that can require even more examination than the standard amount
I do not believe that all welds must be visually examined. Per 341.4.1(2008), for NFS, 5% of fabrication must be examined. for welds, each welders's and weld operators work shall be represented. If you are nor working under Normal Fluid Service, then your have to read the book to see how much to examine.
Finally, if the RT examination requirement is waived in favor of the in-process examination procedure, you have to look at almost everything for those welds
I think that B31.3 will have has its own criterial for weld imperfections (Table 341.3.2 in 2008), and ASME V is only used to define methods and processes of examination.