For functional testing I would not approach software developed for a SaaS model much differently that software developed for sale. You are still going to have a large, diverse user base that are going to find things to do with your software that you didn't think of.
Assuming you are hosting the software, one area that is going to be critical is performance. It doesn't matter how well your software functions if it is slow an unresponsive. Of course, performance will be affected by much more than just the software. This will touch across many areas of your infrastructure such as DB, web servers, app servers, OS, network, hardware...
Other than what Tory said about performance remember that in SaaS you are the Service provider to (hopefully!) thousands of organizations and users, this means that:
1. You are not allowed to have significant down-time when performing version updates or any regular maintenance task.
2. If something goes wrong you need to be able to recover very quickly.
In SaaS companies, these tasks are not part of the IT group since they need to be built into the product and they should be correctly tested by the QA - specially to verify that they work correctly in all scenarios and not only on the main path.
This will depend too much on the requirements you set for these types of registrations.
At times you ONLY validate that the email used to register does not come from a public email service such as gmail, or msn; other times you go as far as asking for a valid credit card and making sure the information provided is correct.
So for this I would go to the person defining this validation and asking him/her what is expected from the system.