I don't deal with many weld spec's, How much NDT and other inspection
is needed on such a wide open material of a36 steel ?
The short answer is: it depends. For the stuff we're discussing here, the wide-open spec of A36 doesn't really matter; you're more concerned with the weld, and most of the weld failures can happen with A36 just as well as with other grades. In general, the NDT requirements for a weld are determined by the criticality of the weld, not by the parent material*.
The general baseline requirement is a visual inspection (VT), which doesn't have to be done by a CWI (Certified Welding Inspector). This one is just common sense; the welds should be looked at to make sure they're good before you ship the part.
The next step up is to require the visual inspection to be done by a CWI. This level is more of a paperwork exercise, having a CWI sign off on it does increase the chances that the visual inspection will actually happen and be done right.
The next step up is to look for surface defects with NDT. This is usually either dye penetrant (PT) on aluminum or mag particle (MT) on steel. This is good, cheap insurance. I've had some weldments done by experienced welders where we found tranverse cracks in fillet welds using MT that were missed in VT. The cost is pretty cheap. We'd get large weldments MT inspected by a third party for about $250 (this was 5 or so years ago).
For even more critical welds, you want to look for defects under the surface. The two main methods are ultrasonic (UT) and x-ray (RT). UT can be cheaper, but doesn't work on thin stuff. RT is the gold standard, but is more of a disruption to use (you need to clear the area). RT also provides a permanent record of the inspection (i.e. the film).
A few other scenarios where NDT can be important even on mild steel/HSLA:
1) when you have a highly-restrained joint with thick sections. When the steel is rolled, any discontinuities get rolled flat, so your transverse (through-plane) strength is lower than either your longitudinal or longitudinal transverse directions. When a thick plate is heavily welded on one side, the stresses from the weld pool solidifying can actually crack the heavy plate internally. This can only be detected by UT or RT. I believe there have been a few structural collapses due to this phenomenon, but I don't know the details off the top of my head.
2) Another weld restraint issue with thick sections can be if you have small cracks near the weld, for example a weld access hole. If the hole is thermally cut it can have small cracks that can be worsened when stressed by weld shrinkage. One technique for dealing with this problem is to grind the thermally cut surfaces and the PT them to ensure there are no cracks.
3) Because the transverse strength of steel plate is not well controlled, it can be risky to weld a padeye to a plate where it's loading the plate transversely. It's better for the padeye to be connected to a web under the plate. If you do have transverse loading of a plate, some lifting equipment standards require either UT/RT (to check for inclusions/delamination) or using special "z-quality" material**.
* There are exceptions, of course. For example, when welding A514/T1 steel, you need to wait at least 48 hours after welding before you NDT.
** I've never actually seen such material, nor have any steel shops I've asked ever seen it, but apparently it does exist.