Describing how much attention you’ve paid to an argument

There seems to be a hole in English (I don’t know about other languages) for efficiently describing how much attention you’ve paid to an argument.

I can think of a variety of amounts and sorts of attention—looks cool and plausible, examined for attractive arguments against the other side, checked math for accuracy, checked math for plausibility of application, looked for counter-arguments, looked for evidence in favor, checked factual material, checked for whether some parts are sound even if there are some errors.....

Any other suggestions for types of attention?