I'm a professional Web designer and I use Flash in moderate quantities. I agree that you should not have an all-Flash Web site or use a "splash page" which is just some useless bit of marketing fluff that annoys people. However, I think Flash has huge potential for educational applications. You can make a Flash movie to demonstrate some complex point or explain visually how something works or what it does. The best use of Flash I've seen so far, for marketing and sales purposes, is a site (sorry, I don't remember what it was) that lets you see mockups of various decorating options for a kitchen or bathroom.
I use Flash on the site I maintain at
www.experioronline.com to help visitors use our contact form. The audience for the site includes a number of people with few Web browsing skills, so I set up these little movies to help them over the hard parts. You can see it at
www.experioronline.com/formhelp2.htm. Click the blue button that says "Demo." You'll note I also provide a No Flash version for those who don't have or don't like it.
If a Flash movie causes a site to load slowly, the Flash designer either doesn't know what he/she is doing or the client insisted on an unrealistically large file. Flash actually should load as quickly or even more quickly than a lot of graphics; it's designed to be very "lightweight" but you have to work at optimizing it, just like a good Web designer works at optimizing the html and other code on the site.
Flash can also be used with databases for some very nice dynamic effects. If you want Flash, I'd reccommend you think of a way to use it that adds value you couldn't get any other way. However, DON'T let anyone make something for you that blinks, flashes, pulses, or oscillates in a repetitive rhythm. Such animations can actually provoke epileptic seizures in those who are vulnerable to them. You want to avoid anything that's like a strobe light whatever you do.