All my work on my portfolio site would be work I created at my day job. Does this look bad to a client?
It won't really be a problem if the work is solid and there is
enough variety to the projects/pieces. If looking for freelance web
design and you only have 10 pages from the same company site to
show, it won't look that favorable. However, if you show 10 pages
from the same company but 6 different designs for 6 different
revenue streams it may be fine.
People/Clients often want to see how you deal with varying challenges and if you can pull off the style of design they are seeking. Freelancing well often requires the designer to be able to complete projects in a variety of styles. If a client is seeking a corporate, sleek, look and all your stuff looks like it's designed for Toys 'R' Us that won't help. Not that Toys "R' Us is bad, just a different audience and style. Conversely, if the client wants "joyful, young, and fun" and all your stuff looks corporate slick they won't be intrigued.
My day job is with a well known organization, should I mention who I work for on my portfolio? Their logo is all over my work so people would know anyway I guess.
It won't have a negative impact to any great degree. In fact, if the company is well known enough it may be favorable. And, as you post yourself, if the logo is all over the place, then they'll know anyway unless you take steps to remove identifiable branding. Showing real-world design solutions is always a good thing to do rather than fabricating designs without real-world restrictions.
Should I clear this with my day job first? What if they see my portfolio online?
It certainly wouldn't do any harm. If you choose not to clear it first, be prepared to have your employment terminated if the company is not happy with their discovery later. And never do any work for a competing organization, even if the company gives you the "okay" to freelance on your off-time.