Next we have UltraSonic(UT) testing. This requires expensive equipment and a good examiner to interpret.
Third we have X-Ray. This is used on welds that are very important as it is also hard to do and interpret. It also requires the weld to be ground smooth to distinguish flaws from ordinary weld.
I am sure there are a variety of other non destructive testing (NDT )techniques. These are the common ones used in industry.
I do want to mention that pressure vessels are hard to make. Especially something so large. This could actually be a design problem and not welds. Pressure vessels are often tested at 5/3 their working pressure. So failures at testing are not uncommon.