In this field, having a diploma or a degree would not differ much. What would matter most would be the portfolio that you would have to present to the potential employer for him to gauge your worth. As a BA and dip holder I find that this is the general trend. One might hold a degree but he might just as well produce crap work while a dip holder could be really creative in his/her thought process.
As a web designer, the job scope is generally to take care of the design, layout, basic coding. Information would already be provided, hence the designer would have to decide on content format, method of presenting that information (by flash, shockwave etc), layout and design (including theme and general style). Most of the time the coding would be done by him as well. While this might seem like an easy task in Dreamweaver, there are many complex issues involved in fine tuning of the coding process.
There are quite a few issues to take notice of, some important ones would be file size, download time, colour depth, file naming conventions and cross-platforming (IE and Netscape). When there are complex table formats, the cross platforming issues really create a headache.
This would be the basic job of a web designer. Basic knowledge of forms, javascript would usually be helpful. Flash and Shockwave programming knowledge is critical, as these vector based media can create really fantastic presentations in a really small amount of space.
Knowledge of other skills like video and sound editing, 3D modelling and animation, would only value add to your worth as a web designer.
Salary wise, the market is not too good now with an abundance of freshies from the polys, but as a dip holder you could be looking at something like S$1.4-1.8k as starting and BA holders $1.8-2.2 starting pay. Again, it will also all depend on the portfolio. There is a very big freelance market out there if you look carefully, but then again, as with many other industries, there are also many students willing to do it at a much reduced rate
PM me if you wish to find out anything more.