Looks good.

Small quirk I found:
When you hover over the "?" for Severity, there is a link to click to get a list of the SLA's, but you can't click it because as soon as you move off the "?" the bubble that contains the link disappears (in Firefox).

-edit-

When I tested with an account with 'self support' the only indication that I couldn't raise a support ticket was:
Support Level: No results match

I think it would be more intuitive if it had a banner at the top eg. "Your current subscription does not include Red Hat support, to purchase support visit the following page link"

Also, when I submit (with the self support account) I get the following error:

Error 404 Not Found Message: {"code":"404","message":"Unknown group"}

Possibly due to the fact that there is no value available in the 'Support Level' drop down?

-last edit-

It would be a nice addition if the 'Severity' drop down provided some insight into the SLA being selected without having to leave the page to look at the table here:
https://access.redhat.com/support/offerings/production/sla.

eg. When you select the severity, based on the subscription level it could provide details on what to expect when selecting that severity.

So in the scenario where I have a premium subscription selected and I select 'Severity 1', a text box below the drop down could provide the detail "Initial Response: 1 hour, Ongoing Response: 1 hour or as agreed", without having to leave the page.

It may already do this (apologies if it does), but as mentioned, I tested with a self support account.