What are the most important things while checking the columns internals

There are two basic things wether you are checking at fabrication stage or checking after equipment has been in operation.

For checking after the equipmnet has been in operation the first and foremost is to check the condition of the shell, for any pitting, corrosion mark, loss of thickness, etc. Check the nozzles for corrosion or any other damage. Check the supporting structurals for any crack, discontinuity, etc. check the sealings are as per the drawing.

If you are checking at fabrication stage pl check if the compliance as per drawing, mock assembly outside the column, material as per drawing, etc.

During installation of Valve trays (such as Glistch make) one should take care to check for horizontality of trays by water tube or other means to get max. accuracy of level usually not more than 1 mm. difference between ends of any diameter of each tray. This depends on the accuracy of fabrication of the supporting rings welded inside the columns and the verticality of erected column in two planes perpendicular to each other. The efficiency of gas liquid interaction will be affected if this is not taken seriously enough.