How do I see the exact information customers filled out in a form?

Hmmm maybe I do not understand you completely. But unless you have salesforce set to capture multiple values (for the same person). If they're using the SAME email it's just going to update the custom fields as they keep submitting (IE: it will only display the most recent info that someone filled out with that email) 

they would need to fill out a NEW email to separate the people.
You can set salesforce to add values to a field. So marketo will just display the most recent. Salesforce will display all values. I think you can do this with a simple Workflow In salesforce. 

Talk to your SF DEV - 

Note that this is not a retroactive solution. 

Yes, it skips any repeats... we only allow Marketo to overwrite certain fields. I just wanted a raw list of what was actually entered into the form so that I can troubleshoot when people don't appear to be registered when they say they completed the form.

You can view the exact form fill by going to the list of leads who filled out this form and then click on the lead ID, then go to the last Filled Out Form log item.

If you're having issues with people filling the form but not being registered, it'd be good to review your sync between your marketo instance and your webinar platform. Are you sending the email from Marketo or from your webinar platform?

I would also recommend simply looking in the activity log of the leads in question that submitted the form.  If you scroll to the time they submitted the form, it should what happened on each corresponding field that might have been updated by the FFO.