If you have Acrobat, and the form does not have any security restrictions, and is not "blessed" with Extended Rights for Reader, you can add comments to the fillable form (I just tested that).
Now, if the form comes with Extended Rights for Reader, you will get an according note, and with Save a Copy…, you can create a version without those rights, and then you can add comments (there is a (for me hard to understand) crosslock between extended rights for filling and saving forms and using comments); blame Adobe for that and submit a feature request.
If there are security restrictions, and you are not the creator of the form, you'd have to get to its issuer and persuade them to send you an unlocked version (or let the search engines be your friend).
There is one more possibility, and that is when the form is not a PDF form, but an XFA form wrapped in a PDF (this form has been created using LiveCycle Designer). In this case, you may be completely out of luck (has to be confirmed).
All the above is when you use Acrobat.
If you use Reader, you better update to Reader XI, which has most of the limitations where Extended Rights are needed lifted. In this case, the above comments should apply as well.
With an older Reader version, the only suggestion I have is to update, because there the crosslock mentioned becomes active.
One more advice: Don't be tempted to use Preview.app to add the comments; when saving the form, Preview.app will thoroughly destroy the form, so that it won't be usable anymore in Acrobat (the only thing you can do to salvage it is to try to export the data and import it again in a blank form).