Enter Design View on the subform you'd like to change. Open the Properties window, select the Detail item, go to the Event tab, push the "..." button next to "On Click" and enter the following line of code:
DoCmd.GoToRecord , , acNext
Add in any error handling code you'd like. Now whenever you click on the form itself you will move to the next record, but you will still be able to edit the text boxes. If you want to make the text boxes uneditable and have clicking on them advance to the next record too, simply add a transparent "Next Record" command button over the entire form.
Edit: Change acNext to acNewRec if you want it to go to a blank record, and use the first solution I listed instead of the 2nd.