How can I enable form user to insert comments at any point as they fill in the form?

I'd like to accomplish this without adding random text boxes everywhere.

Please check the Configurable List widget. 

link: http://widgets.jotform.com/widget/configurable_list

user guide: -How-to-Set-Up-the-Configurable-List-Widget

You can add TextArea field in the Configurable List for the comment input.

OR

If comments can be condensed to one liner only (for simpler purpose), perhaps the Field Multiplier widget will suffice.

link: http://widgets.jotform.com/widget/field_multiplier

test form: http://form.jotformpro.com/form/50541619595966?

Hope this help. Let us know if you need further assistance.