my first thought is that its unwise to reuse object names haphazardly.
param_table is sometimes a reactiveValues, but also a ui output (output$param_table)
My second though is that you nest a lot of reactivity that probably doesnt need to be nested.
You also use a global assignment that is probably more trouble than its worth...
For the best support please consider providing a reprex.
(Shiny debugging and reprex guide)